import java.util.*;
import java.util.zip.*;
import java.util.List;
import java.util.regex.*;
import java.util.concurrent.*;
import java.util.concurrent.atomic.*;
import java.util.concurrent.locks.*;
import java.util.function.*;
import javax.swing.*;
import javax.swing.event.*;
import javax.swing.text.*;
import javax.swing.table.*;
import java.io.*;
import java.net.*;
import java.lang.reflect.*;
import java.lang.ref.*;
import java.lang.management.*;
import java.security.*;
import java.security.spec.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import java.awt.geom.*;
import javax.imageio.*;
import java.math.*;
import java.time.Duration;
import java.lang.invoke.VarHandle;
import java.lang.invoke.MethodHandles;
// Abstract base class for finding all connected regions of same color
// in an image using flood filling

import java.text.NumberFormat;
import java.awt.geom.*;
import static x30_pkg.x30_util.DynamicObject;
import java.text.*;
import java.util.TimeZone;

class main {

abstract static class AbstractFastRegions<Img extends WidthAndHeight> implements Runnable, IImageRegions<Img> , IFieldsToList{
  Img image;
  AbstractFastRegions() {}
  AbstractFastRegions(Img image) {
  this.image = image;}public Object[] _fieldsToList() { return new Object[] {image}; }

  int w, h; // Image size
  int runner; // Position in image currently being scanned
   final public int getSize(){ return size(); }
public int size() { return size; }
 int size; // =w*h
  
  IntBuffer stack = new IntBuffer(); // locations as y*w+x
   final public int[] getRegionMatrix(){ return regionMatrix(); }
public int[] regionMatrix() { return regionMatrix; }
 int[] regionMatrix; // for each pixel: region index (starting at 1)
  IntBuffer regionPixels = new IntBuffer(); // collect all pixels for regions
  
   final public AbstractFastRegions<Img > setWithDiagonals(boolean withDiagonals){ return withDiagonals(withDiagonals); }
public AbstractFastRegions<Img > withDiagonals(boolean withDiagonals) { this.withDiagonals = withDiagonals; return this; }  final public boolean getWithDiagonals(){ return withDiagonals(); }
public boolean withDiagonals() { return withDiagonals; }
 boolean withDiagonals = false; // also walk diagonally?
  
  // initialize these to use them
  
  IntBuffer regionFirstPixel = new IntBuffer(); // for each region: index of first pixel found in regionPixels
  IntBuffer regionSize = new IntBuffer(); // for each region: number of pixels
  IntBuffer regionBounds = new IntBuffer(); // for each region: bounds (x1, y1, x2, y2)
  
  // index = dual log of region size, value = region index
  List<IntBuffer> regionsBySize = new ArrayList();
  
  int regionCounter;
  boolean verbose = false;
  
  // temporary
  int currentColor;
  
  double regionStep = .1; // for rendering in regionsImage
  
  int x(int pos) { return pos % w; }
  int y(int pos) { return pos / w; }
  int pos(int x, int y) { return y*w+x; }
  Pt pt(int pos) { return new Pt(x(pos), y(pos)); }
  boolean validPos(int x, int y) { return x >= 0 && y >= 0 && x < w && y < h; }
  
  abstract int getColor(int pos);
  
  boolean initialized() { return regionMatrix != null; }
  
  void init() {
    if (initialized()) return;
    
    w = image.getWidth(); h = image.getHeight();
    size = w*h;
    regionMatrix = new int[size];
    
    // 0 entries are unused
    { if (regionFirstPixel != null) regionFirstPixel.add(0); } 
    { if (regionSize != null) regionSize.add(0); }
    
    { if (regionPixels != null) regionPixels.setSize(size); }
  }
  
  // Search for all regions in scanline order
  public void run() { try {
    if (initialized()) return;
    init();
    
    while (runner < size) {
      if (regionMatrix[runner] == 0)
        makeRegion();
      ++runner;
    }
  } catch (Exception __e) { throw rethrow(__e); } }
  
  // returns index of new region
  int makeRegion() {
    // make a new region, get color
    int region = ++regionCounter;
    { if (regionFirstPixel != null) regionFirstPixel.add(regionPixels != null ? l(regionPixels) : runner); }
    currentColor = getColor(runner);
    stack.add(runner);
    int rsize = 0, x1 = w, y1 = h, x2 = 0, y2 = 0;
    

    // flood-fill region
    while (nempty(stack)) {
      int pos = stack.popLast();
      if (regionMatrix[pos] != 0) continue; // check again if set in the meantime (color has been checked before)

      // new pixel found!
      int x = x(pos), y = y(pos);
      
      // march to the left
      int lineStart = pos-x;
      int xLeft = x;
      while (xLeft > 0 && addable(lineStart+xLeft-1))
        --xLeft;
        
      // march to the right
      int xRight = x+1;
      while (xRight < w && addable(lineStart+xRight))
        ++xRight;
      
      // Now we know [xLeft; xRight) are our pixels
      // mark them in matrix
      for (x = xLeft; x < xRight; x++) {
        regionMatrix[lineStart+x] = region;
        { if (regionPixels != null) regionPixels.add(lineStart+x); }
      }
        
      // increase region size
      rsize += xRight-xLeft;
      
      
      
      // update bounds
      if (xLeft < x1) x1 = xLeft;
      if (xRight-1 > x2) x2 = xRight-1;
      if (y < y1) y1 = y;
      if (y > y2) y2 = y;
      
      // explore above & below
      int xLeft2 = withDiagonals ? max(0, xLeft-1) : xLeft;
      int xRight2 = withDiagonals ? min(w, xRight+1) : xRight;
      if (y > 0)
        addStreaks(lineStart-w, xLeft2, xRight2);
      if (y < h-1)
        addStreaks(lineStart+w, xLeft2, xRight2);
    }
    
    { if (regionSize != null) regionSize.add(rsize); }
    { if (regionBounds != null) regionBounds.addAll(x1, y1, x2+1, y2+1); }
    if (regionsBySize != null) {
      int iBucket = dualLog(rsize);
      var buffer = listGetOrCreate(regionsBySize, iBucket, () -> new IntBuffer());
      buffer.add(region);
    }
    
    return region;
  }
  
  boolean addable(int pos) {
    if (regionMatrix[pos] != 0) return false; // touching myself (or someone else)
    if (getColor(pos) != currentColor) return false; // wrong color
    return true;
  }
  
  boolean addToStack(int pos) {
    if (!addable(pos)) return false;
    stack.add(pos);
    return true;
  }
  
  void addStreaks(int lineStart, int xLeft, int xRight) {
    int x = xLeft;
    while (x < xRight) {
      if (addToStack(lineStart+x))
        while (x+1 < xRight && addable(lineStart+x+1))
          ++x;
      ++x;
    }
  }

  IBWImage regionsImage() {
    return iBWImageFromFunction((x, y) -> {
      var region = regionMatrix[pos(x, y)];
      return ((region-1)*regionStep) % (1.0+regionStep-0.0001);
    }, w, h);
  }
  
  final public int nRegions(){ return regionCount(); }
public int regionCount() { return regionCounter; }
  
  abstract class RegionIterator {
    int pos;
    
    abstract boolean next();
    
    int pos() { return pos; }
    int x() { return AbstractFastRegions.this.x(pos); }
    int y() { return AbstractFastRegions.this.y(pos); }
    
    int[] pixelsAsIntArray() { throw todo(); }
  }
  
  // returns points in no particular order
  class FloodRegionIterator extends RegionIterator {
    int region;
    IntBuffer stack = new IntBuffer(); // locations as y*w+x
    BitSet seen = new BitSet(size);
    
    FloodRegionIterator(int region) {
  this.region = region;
      int pos = regionFirstPixel.get(region);
      printVars("region", region, "pos", pos);
      seen.set(pos);
      stack.add(pos);
    }
    
    // flood-fill region
    boolean next() {
      if (empty(stack)) return false;
      
      pos = stack.popLast();

      // explore neighborhood
      int x = x(), y = y();
      if (x > 0)   tryPosition(pos-1);
      if (x < w-1) tryPosition(pos+1);
      if (y > 0)   tryPosition(pos-w);
      if (y < h-1) tryPosition(pos+w);

      return true;
    }
    
    private void tryPosition(int p) {
      if (!seen.get(p) && regionMatrix[p] == region) {
        seen.set(p);
        stack.add(p);
      }
    }
  }
  
  class CachedRegionIterator extends RegionIterator {
    int i, to;

    CachedRegionIterator(int region) {
      i = regionFirstPixel.get(region);
      to = region+1 < l(regionFirstPixel) ? regionFirstPixel.get(region+1) : l(regionPixels);
      
      
    }
    
    boolean next() {
      if (i >= to) return false;
      pos = regionPixels.get(i++);
      return true;
    }
    
    int[] pixelsAsIntArray() {
      return regionPixels.subArray(i, to);
    }
  }
  
  int regionSize(int iRegion) { return regionSize.get(iRegion); }
  
  final Pt firstPixel(int iRegion){ return samplePixel(iRegion); }
Pt samplePixel(int iRegion) {
    return pt(firstPixelPos(iRegion));
  }
  
  int firstPixelPos(int iRegion) {
    int i = regionFirstPixel.get(iRegion);
    return regionPixels != null ? regionPixels.get(i) : i;
  }
  
  boolean inRegion(int iRegion, int x, int y) {
    return validPos(x, y) && regionMatrix[pos(x, y)] == iRegion;
  }
  Rect regionBounds(int iRegion) { return rectFromPoints(
    regionBounds.get((iRegion-1)*4),
    regionBounds.get((iRegion-1)*4+1),
    regionBounds.get((iRegion-1)*4+2),
    regionBounds.get((iRegion-1)*4+3)); }
  
  int regionAt(Pt p) { return regionAt(p.x, p.y); }
  
  int regionAt(int x, int y) {
    return !validPos(x, y) ? 0 : regionMatrix[pos(x, y)];
  }
  
  int regionAt(int pos) {
    return regionMatrix[pos];
  }
  
  RegionIterator regionIterator(int iRegion) {
    return regionPixels != null
      ? new CachedRegionIterator(iRegion)
      : new FloodRegionIterator(iRegion);
  }
  
  List<Pt> regionPixels(int iRegion) {
    var it = regionIterator(iRegion);
    List<Pt> l = new ArrayList();
    while (it.next())
      l.add(new Pt(it.x(), it.y()));
    return l;
  }
  
  // select extra features before regions are made
  // (not necessary anymore)
  
  void collectFirstPixels() { /*regionFirstPixel = new IntBuffer;*/ }
  void collectBounds() { /*regionBounds = new IntBuffer;*/ }
  
  Matrix<Boolean> regionBitMatrix(int iRegion) {
    return new AbstractMatrix<Boolean>(w, h) {
      public Boolean get(int x, int y) {
        return inRegion(iRegion, x, y);
      }
    };
  }
  
  void markRegionInPixelArray(int[] pixels, int iRegion, int rgba) {
    if (iRegion <= 0) return;
    for (int i = 0; i < l(pixels); i++)
      if (regionAt(i) == iRegion)
        pixels[i] = rgba;
  }
  
  List<Integer> regionIndices() { return virtualCountList(1, nRegions()+1); }
  
  IterableIterator<Integer> regionsRoughlyByDecreasingSize() {
    return nestedIterator(countIterator_inclusive_backwards(regionsBySize.size()-1, 0),
      iBucket -> iterator(regionsBySize.get(iBucket)));
  }
  
  final public IImageRegion<Img> get(int iRegion){ return getRegion(iRegion); }
public IImageRegion<Img> getRegion(int iRegion) {
    return new ImageRegion(iRegion);
  }
  
  final public List<IImageRegion<Img>> get(){ return regions(); }
public List<IImageRegion<Img>> regions() {
    run();
    return listFromFunction(i -> getRegion(i+1), nRegions());
  }
  
  class ImageRegion implements IImageRegion<Img> , IFieldsToList{
  int iRegion;
  ImageRegion() {}
  ImageRegion(int iRegion) {
  this.iRegion = iRegion;}public Object[] _fieldsToList() { return new Object[] {iRegion}; }

    public int hashCode() { return iRegion; }
    public boolean equals(Object o) {
      if (!(o instanceof AbstractFastRegions.ImageRegion)) return false;
      return ((AbstractFastRegions.ImageRegion) o).creator() == creator()
        && ((AbstractFastRegions.ImageRegion) o).iRegion == iRegion;
    }
    
    public Img image() { return image; }
    public Object creator() { return AbstractFastRegions.this; }
    public int indexInCreator() { return iRegion; }
    public Boolean createdWithDiagonals() { return withDiagonals; }
  
    public Rect bounds() { return regionBounds(iRegion); }
    
    public int numberOfPixels() { return regionSize(iRegion); }
    
    public Pt firstPixel() { return pt(firstPixelPos()); }
    public int firstPixelPos() { return AbstractFastRegions.this.firstPixelPos(iRegion); }
    
    public IterableIterator<Pt> pixelIterator() {
      var it = regionIterator(iRegion);
      return iteratorFromFunction(() -> it.next() ? pt(it.pos()) : null);
    }
    
    public int[] pixelsAsIntArray() {
      return regionIterator(iRegion).pixelsAsIntArray();
    }
    
    public boolean contains(int x, int y) { return inRegion(iRegion, x, y); }
    
    public Color color() {
      return toColor(rgbForRegion(this));
    }
    
    final public int firstPixelLogicalColor(){ return brightness(); }
public int brightness() {
      return getColor(firstPixelPos());
    }
    
    public String toString() {
      return renderRecordVars("Region", "brightness", brightness(), "color", color(), "pixels" , numberOfPixels(), "bounds", bounds());
    }
  }
  
  abstract RGB rgbForRegion(ImageRegion r);
  
  public Img image() { return image; }
  
  // called after scan was performed externally
  void markDone() { runner = size; }
}
static RuntimeException rethrow(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  throw t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}

static RuntimeException rethrow(String msg, Throwable t) {
  throw new RuntimeException(msg, t);
}


static int l(Object[] a) { return a == null ? 0 : a.length; }
static int l(boolean[] a) { return a == null ? 0 : a.length; }
static int l(byte[] a) { return a == null ? 0 : a.length; }
static int l(short[] a) { return a == null ? 0 : a.length; }
static int l(long[] a) { return a == null ? 0 : a.length; }
static int l(int[] a) { return a == null ? 0 : a.length; }
static int l(float[] a) { return a == null ? 0 : a.length; }
static int l(double[] a) { return a == null ? 0 : a.length; }
static int l(char[] a) { return a == null ? 0 : a.length; }
static int l(Collection c) { return c == null ? 0 : c.size(); }

static int l(Iterator i) { return iteratorCount_int_close(i); } // consumes the iterator && closes it if possible

static int l(Map m) { return m == null ? 0 : m.size(); }
static int l(CharSequence s) { return s == null ? 0 : s.length(); }
static long l(File f) { return f == null ? 0 : f.length(); }






  static int l(IMultiMap mm) { return mm == null ? 0 : mm.size(); }











  static int l(IntBuffer b) { return b == null ? 0 : b.size(); }



  static int l(LongBuffer b) { return b == null ? 0 : b.size(); }







  static int l(IntSize o) { return o == null ? 0 : o.size(); }




static Color getColor(BufferedImage img, int x, int y) {
  return colorFromRGBA(img.getRGB(x, y));
}

static Color getColor(BufferedImage img, Pt p) {
  return colorFromRGBA(img.getRGB(p.x, p.y));
}


static boolean nempty(Collection c) {
  return !empty(c);
}

static boolean nempty(CharSequence s) {
  return !empty(s);
}

static boolean nempty(Object[] o) { return !empty(o); }
static boolean nempty(byte[] o) { return !empty(o); }
static boolean nempty(int[] o) { return !empty(o); }

static boolean nempty(BitSet bs) { return !empty(bs); }

static boolean nempty(Map m) {
  return !empty(m);
}

static boolean nempty(Iterator i) {
  return i != null && i.hasNext();
}


static boolean nempty(IMultiMap mm) { return mm != null && mm.size() != 0; }



static boolean nempty(Object o) { return !empty(o); }





static boolean nempty(IntBuffer b) { return b != null && !b.isEmpty(); }



static boolean nempty(LongBuffer b) { return b != null && !b.isEmpty(); }



static boolean nempty(Rect r) { return r != null && r.w != 0 && r.h != 0; }






static boolean nempty(IntSize l) { return l != null && l.size() != 0; }


static int max(int a, int b) { return Math.max(a, b); }
static int max(int a, int b, int c) { return max(max(a, b), c); }
static long max(int a, long b) { return Math.max((long) a, b); }
static long max(long a, long b) { return Math.max(a, b); }
static double max(int a, double b) { return Math.max((double) a, b); }
static float max(float a, float b) { return Math.max(a, b); }
static double max(double a, double b) { return Math.max(a, b); }

static <A extends Comparable<A>> A max (Iterable<A> l) {
  A max = null;
  var it = iterator(l);
  if (it.hasNext()) {
    max = it.next();
    while (it.hasNext()) {
      A a = it.next();
      if (cmp(a, max) > 0)
        max = a;
    }
  }
  return max;
}

/*Nah.
static int max(Collection<Integer> c) {
  int x = Integer.MIN_VALUE;
  for (int i : c) x = max(x, i);
  ret x;
}*/

static double max(double[] c) {
  if (c.length == 0) return Double.MIN_VALUE;
  double x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static float max(float[] c) {
  if (c.length == 0) return Float.MAX_VALUE;
  float x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static byte max(byte[] c) {
  byte x = -128;
  for (byte d : c) if (d > x) x = d;
  return x;
}

static short max(short[] c) {
  short x = -0x8000;
  for (short d : c) if (d > x) x = d;
  return x;
}

static int max(int[] c) {
  int x = Integer.MIN_VALUE;
  for (int d : c) if (d > x) x = d;
  return x;
}

static <A extends Comparable<A>> A max(A a, A b) {
  return cmp(a, b) >= 0 ? a : b;
}


static int min(int a, int b) {
  return Math.min(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }

static double min(double a, double b) {
  return Math.min(a, b);
}

static double min(double[] c) {
  double x = Double.MAX_VALUE;
  for (double d : c) x = Math.min(x, d);
  return x;
}

static float min(float[] c) {
  float x = Float.MAX_VALUE;
  for (float d : c) x = Math.min(x, d);
  return x;
}

static byte min(byte[] c) {
  byte x = 127;
  for (byte d : c) if (d < x) x = d;
  return x;
}

static short min(short[] c) {
  short x = 0x7FFF;
  for (short d : c) if (d < x) x = d;
  return x;
}

static int min(int[] c) {
  int x = Integer.MAX_VALUE;
  for (int d : c) if (d < x) x = d;
  return x;
}

static <A extends Comparable<A>> A min(A a, A b) {
  return cmp(a, b) <= 0 ? a : b;
}


static int dualLog(int i) {
  return 32-Integer.numberOfLeadingZeros(max(0, i-1));
}


static <A> A listGetOrCreate(List<A> l, int i, Class<? extends A> c) {
  return listGetOrCreate(l, i, () -> nuInstance(c));
}

static <A> A listGetOrCreate(List<A> l, int i, IF0<A> f) {
  if (l == null) return null;
  A a = get(l, i);
  if (a == null)
    listSet(l, i, a = f.get());
  return a;
}

static <A> A listGetOrCreate(Class<? extends A> c, List<A> l, int i) {
  return listGetOrCreate(l, i, c);
}


static IBWImage iBWImageFromFunction(IF2_IntInt_Double f, int w, int h) {
  return new IBWImage() {
    public int getWidth() { return w; }
    public int getHeight() { return h; }
    
    public float getFloatPixel(int x, int y) {
      return (float) f.get(x, y);
    }
  };
}


  static RuntimeException todo() {
    throw new RuntimeException("TODO");
  }
  
  static RuntimeException todo(Object msg) {
    throw new RuntimeException("TODO: " + msg);
  }


// Use like this: printVars(+x, +y);
// Or: printVars("bla", +x);
// Or: printVars bla(, +x);
static void printVars(Object... params) {
  printVars_str(params);
}


static boolean empty(Collection c) { return c == null || c.isEmpty(); }
static boolean empty(Iterable c) { return c == null || !c.iterator().hasNext(); }
static boolean empty(CharSequence s) { return s == null || s.length() == 0; }
static boolean empty(Map map) { return map == null || map.isEmpty(); }
static boolean empty(Object[] o) { return o == null || o.length == 0; }
static boolean empty(BitSet bs) { return bs == null || bs.isEmpty(); }


static boolean empty(Object o) {
  if (o instanceof Collection) return empty((Collection) o);
  if (o instanceof String) return empty((String) o);
  if (o instanceof Map) return empty((Map) o);
  if (o instanceof Object[]) return empty((Object[]) o);
  if (o instanceof byte[]) return empty((byte[]) o);
  if (o == null) return true;
  throw fail("unknown type for 'empty': " + getType(o));
}


static boolean empty(Iterator i) { return i == null || !i.hasNext(); }

static boolean empty(double[] a) { return a == null || a.length == 0; }
static boolean empty(float[] a) { return a == null || a.length == 0; }
static boolean empty(int[] a) { return a == null || a.length == 0; }
static boolean empty(long[] a) { return a == null || a.length == 0; }
static boolean empty(byte[] a) { return a == null || a.length == 0; }
static boolean empty(short[] a) { return a == null || a.length == 0; }




static boolean empty(IMultiMap mm) { return mm == null || mm.size() == 0; }


static boolean empty(File f) { return getFileSize(f) == 0; }






static boolean empty(IntBuffer b) { return b == null || b.isEmpty(); }



static boolean empty(LongBuffer b) { return b == null || b.isEmpty(); }















static boolean empty(Rect r) { return !(r != null && r.w != 0 && r.h != 0); }



static boolean empty(Chain c) { return c == null; }



static boolean empty(AppendableChain c) { return c == null; }


static boolean empty(IntSize l) { return l == null || l.size() == 0; }


static Pt pt(int x, int y) {
  return new Pt(x, y);
}

static Pt pt(int x) {
  return new Pt(x, x);
}


static Rect rectFromPoints(int x1, int y1, int x2, int y2) {
  return pointsRect(x1, y1, x2, y2);
}

static Rect rectFromPoints(Pt a, Pt b) {
  return pointsRect(a.x, a.y, b.x, b.y);
}


// get purpose 1: access a list/array/map (safer version of x.get(y))

static <A> A get(List<A> l, int idx) {
  return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}

// seems to conflict with other signatures
/*static <A, B> B get(Map<A, B> map, A key) {
  ret map != null ? map.get(key) : null;
}*/

static <A> A get(A[] l, int idx) {
  return idx >= 0 && idx < l(l) ? l[idx] : null;
}

// default to false
static boolean get(boolean[] l, int idx) {
  return idx >= 0 && idx < l(l) ? l[idx] : false;
}

// get purpose 2: access a field by reflection or a map

static Object get(Object o, String field) {
  try {
    if (o == null) return null;
    if (o instanceof Class) return get((Class) o, field);
    
    if (o instanceof Map)
      return ((Map) o).get(field);
      
    Field f = getOpt_findField(o.getClass(), field);
    if (f != null) {
      makeAccessible(f);
      return f.get(o);
    }
      
    
      if (o instanceof DynamicObject)
        return getOptDynOnly(((DynamicObject) o), field);
    
  } catch (Exception e) {
    throw asRuntimeException(e);
  }
  throw new RuntimeException("Field '" + field + "' not found in " + o.getClass().getName());
}

static Object get_raw(String field, Object o) {
  return get_raw(o, field);
}

static Object get_raw(Object o, String field) { try {
  if (o == null) return null;
  Field f = get_findField(o.getClass(), field);
  makeAccessible(f);
  return f.get(o);
} catch (Exception __e) { throw rethrow(__e); } }

static Object get(Class c, String field) {
  try {
    Field f = get_findStaticField(c, field);
    makeAccessible(f);
    return f.get(null);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Field get_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Static field '" + field + "' not found in " + c.getName());
}

static Field get_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Field '" + field + "' not found in " + c.getName());
}

static Object get(String field, Object o) {
  return get(o, field);
}

static boolean get(BitSet bs, int idx) {
  return bs != null && bs.get(idx);
}


static List<Integer> virtualCountList(int n) {
  return new RandomAccessAbstractList<Integer>() {
    public int size() { return n; }
    public Integer get(int i) { return i; }
  };
}

// to is exclusive
static List<Integer> virtualCountList(int from, int to) {
  int n = max(to-from, 0);
  return new RandomAccessAbstractList<Integer>() {
    public int size() { return n; }
    public Integer get(int i) { return from+i; }
  };
}


static String nRegions(long n) { return n2(n, "region"); }
static String nRegions(Collection l) { return nRegions(l(l)); }
static String nRegions(Map map) { return nRegions(l(map)); }


// TODO: clean up these type signatures?

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(Iterable<A> c, final F1<A, C> makeInnerIterator) {
  return nestedIterator(iterator(c), makeInnerIterator);
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(Iterable<A> c, IF1<A, C> makeInnerIterator) {
  return nestedIterator(iterator(c), makeInnerIterator);
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(IterableIterator<A> c, IF1<A, C> makeInnerIterator) {
  return nestedIterator((Iterator<A>) c, makeInnerIterator);
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(Iterator<A> it1, IF1<A, C> makeInnerIterator) {
  if (it1 == null || !it1.hasNext()) return emptyItIt();
  return iff(new F0() {
    A a;
    Iterator<B> innerIterator;
    
    { nextOuter(); }
    
    void nextOuter() {
      a = it1.next();
      innerIterator = makeInnerIterator.get(a);
    }
    
    public Object get() {
      while (true) { ping();
        if (innerIterator != null && innerIterator.hasNext())
          return innerIterator.next();
        if (!it1.hasNext()) return endMarker();
        nextOuter();
      }
    }
  });
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(final Iterator<A> it1, F1<A, C> makeInnerIterator) {
  if (it1 == null || !it1.hasNext()) return emptyItIt();
  return iff(new F0() {
    A a;
    Iterator<B> innerIterator;
    
    { nextOuter(); }
    
    void nextOuter() {
      a = it1.next();
      innerIterator = makeInnerIterator.get(a);
    }
    
    public Object get() {
      while (true) { ping();
        if (innerIterator != null && innerIterator.hasNext())
          return innerIterator.next();
        if (!it1.hasNext()) return endMarker();
        nextOuter();
      }
    }
  });
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(IF1<A, C> makeInnerIterator, Iterator<A> it1) {
  return nestedIterator(it1, makeInnerIterator);
}

static <A, B, C extends Iterator<B>> IterableIterator<B> nestedIterator(IF1<A, C> makeInnerIterator, Collection<A> l) {
  return nestedIterator(l, makeInnerIterator);
}


static IterableIterator<Integer> countIterator_inclusive_backwards(int a, int b) {
  return new IterableIterator<Integer>() {
    int i = a;
    
    public boolean hasNext() { return i >= b; }
    public Integer next() { return i--; }
  };
}

static <A> IterableIterator<A> countIterator_inclusive_backwards(int a, int b, IF1<Integer, A> f) {
  return mapI_if1(f, countIterator_inclusive_backwards(a, b));
}


static <A> Iterator<A> iterator(Iterable<A> c) {
  return c == null ? emptyIterator() : c.iterator();
}


static Class run(String progID, String... args) {
  Class main = hotwire(progID);
  
  callMain(main, args);
  return main;
}


static class ListFromFunction<A> extends RandomAccessAbstractList<A> implements IFieldsToList{
  int n;
  IF1<Integer, A> f;
  ListFromFunction() {}
  ListFromFunction(int n, IF1<Integer, A> f) {
  this.f = f;
  this.n = n;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + n + ", " + f + ")"; }public Object[] _fieldsToList() { return new Object[] {n, f}; }

  public int size() { return n; }
  public A get(int i) { return f.get(i); }
}

static <A> List<A> listFromFunction(int n, IF1<Integer, A> f) {
  return new ListFromFunction<A>(n, f);
}

static <A> List<A> listFromFunction(IF1<Integer, A> f, int n) {
  return new ListFromFunction<A>(n, f);
}


static WeakReference<Object> creator_class;

static Object creator() {
  return creator_class == null ? null : creator_class.get();
}


static IterableIterator<Pt> pixelIterator(Rect r) {
  return new IterableIterator<Pt>() {
    int x2 = r.x2(), y2 = r.y2();
    int x = r.x, y = r.y;
    
    public boolean hasNext() {
      return y < y2 && x < x2;
    }
    
    public Pt next() {
      Pt p = pt(x, y);
      if (++x >= x2) { x = r.x; ++y; }
      return p;
    }
  };
}


// f: func -> A (stream ends when f returns null)
static <A> IterableIterator<A> iteratorFromFunction(final Object f) {
  class IFF extends IterableIterator<A> {
    A a;
    boolean done = false;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      return _a;
    }
    
    void getNext() {
      if (done || a != null) return;
      a = (A) callF(f);
      done = a == null;
    }
  };
  return new IFF();
}

// optimized version for F0 argument

static <A> IterableIterator<A> iteratorFromFunction(F0<A> f) {
  return iteratorFromFunction_f0(f);
}


static <A> IterableIterator<A> iteratorFromFunction(IF0<A> f) {
  return iteratorFromFunction_if0(f);
}


static java.awt.Color color(String hex) {
  return awtColor(hex);
}



static Color toColor(RGB rgb) {
  return rgb == null ? null : rgb.getColor();
}


static Color toColor(int rgb) {
  return new Color(rgb);
}

static Color toColor(String hex) {
  return awtColor(hex);
}

static Color toColor(int[] rgb) {
  return new Color(rgb[0], rgb[1], rgb[2]);
}


// Use like this: renderRecordVars("MyRecord", +x, +y)
static String renderRecordVars(String recordName, Object... params) {
  List<String> l = new ArrayList();
  int i = 0;
  for (; i+1 < l(params); i += 2)
    l.add(params[i] + "=" + params[i+1]);
  return formatFunctionCall(recordName, l);
}




static void _handleError(Error e) {
  //call(javax(), '_handleError, e);
}


static <A> int iteratorCount_int_close(Iterator<A> i) { try {
  int n = 0;
  if (i != null) while (i.hasNext()) { i.next(); ++n; }
  if (i instanceof AutoCloseable) ((AutoCloseable) i).close();
  return n;
} catch (Exception __e) { throw rethrow(__e); } }


static Color colorFromRGBA(int rgba) {
  return new Color(rgba, true);
}


static int cmp(Number a, Number b) {
  return a == null ? b == null ? 0 : -1 : cmp(a.doubleValue(), b.doubleValue());
}

static int cmp(double a, double b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(int a, int b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(long a, long b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(Object a, Object b) {
  if (a == null) return b == null ? 0 : -1;
  if (b == null) return 1;
  return ((Comparable) a).compareTo(b);
}


static <A> A nuInstance(Class<A> c) {
  return nuEmptyObject(c);
}


static <A> void listSet(List<A> l, int i, A a, A emptyElement) {
  if (i < 0) return;
  while (i >= l(l)) l.add(emptyElement);
  l.set(i, a);
}

static <A> void listSet(List<A> l, int i, A a) {
  listSet(l, i, a, null);
}



// Use like this: printVars_str(+x, +y);
// Or: printVars("bla", +x);
// Or: printVars bla(+x);
static void printVars_str(Object... params) {
  print(renderVars_str(params));
}


static RuntimeException fail() { throw new RuntimeException("fail"); }
static RuntimeException fail(Throwable e) { throw asRuntimeException(e); }
static RuntimeException fail(Object msg) { throw new RuntimeException(String.valueOf(msg)); }


static RuntimeException fail(Object... objects) { throw new Fail(objects); }


static RuntimeException fail(String msg) { throw new RuntimeException(msg == null ? "" : msg); }
static RuntimeException fail(String msg, Throwable innerException) { throw new RuntimeException(msg, innerException); }



static String getType(Object o) {
  return getClassName(o);
}


static long getFileSize(String path) {
  return path == null ? 0 : new File(path).length();
}

static long getFileSize(File f) {
  return f == null ? 0 : f.length();
}


static Rect pointsRect(int x1, int y1, int x2, int y2) {
  return new Rect(x1, y1, x2-x1, y2-y1);
}


static Field getOpt_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}


static Field makeAccessible(Field f) {
  try {
    f.setAccessible(true);
  } catch (Throwable e) {
    // Note: The error reporting only works with Java VM option --illegal-access=deny
    
    vmBus_send("makeAccessible_error", e, f);
    
  }
  return f;
}

static Method makeAccessible(Method m) {
  try {
    m.setAccessible(true);
  } catch (Throwable e) {
    
    vmBus_send("makeAccessible_error", e, m);
    
  }
  return m;
}

static Constructor makeAccessible(Constructor c) {
  try {
    c.setAccessible(true);
  } catch (Throwable e) {
    
    vmBus_send("makeAccessible_error", e, c);
    
  }
  return c;
}


static Object getOptDynOnly(DynamicObject o, String field) {
  if (o == null || o.fieldValues == null) return null;
  return o.fieldValues.get(field);
}


static RuntimeException asRuntimeException(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}


static String n2(long l) { return formatWithThousands(l); }
static String n2(AtomicLong l) { return n2(l.get()); }
static String n2(Collection l) { return n2(l(l)); }
static String n2(Map map) { return n2(l(map)); }

static String n2_getPlural(String singular) {
  //ret singular + "s";
  return plural(singular);
}

static String n2(double l, String singular) {
  return empty(singular) ? str(l) : n2(l, singular, n2_getPlural(singular));
}

static String n2(double l, String singular, String plural) {
  if (fraction(l) == 0)
    return n2((long) l, singular, plural);
  else
    return l + " " + plural;
}

static String n2(long l, String singular, String plural) {
  return n_fancy2(l, singular, plural);
}

static String n2(long l, String singular) {
  return empty(singular) ? n2(l) : n_fancy2(l, singular, n2_getPlural(singular));
}

static String n2(Collection l, String singular) {
  return n2(l(l), singular);
}

static String n2(Collection l, String singular, String plural) {
  return n_fancy2(l, singular, plural);
}

static String n2(Map m, String singular, String plural) {
  return n_fancy2(m, singular, plural);
}

static String n2(Map m, String singular) {
  return n2(l(m), singular);
}

static String n2(long[] a, String singular) { return n2(l(a), singular); }

static String n2(Object[] a, String singular) { return n2(l(a), singular); }
static String n2(Object[] a, String singular, String plural) { return n_fancy2(a, singular, plural); }




  static String n2(IMultiMap mm, String singular) { return n2(mm, singular, n2_getPlural(singular)); }
static String n2(IMultiMap mm, String singular, String plural) {
    return n_fancy2(l(mm), singular, plural);
  }





static <A> IterableIterator<A> emptyItIt() {
  return emptyIterableIterator();
}


// f: func -> A | endMarker
static <A> IterableIterator<A> iff(Object f) {
  return iteratorFromFunction_withEndMarker(f);
}

// can't use type parameter because end marker
static IterableIterator iff(F0 f) {
  return iteratorFromFunction_withEndMarker(f);
}

static <A> IterableIterator iff(IF0 f) {
  return iteratorFromFunction_withEndMarker(f);
}




// legacy mode





//sbool ping_actions_shareable = true;
static volatile boolean ping_pauseAll = false;
static int ping_sleep = 100; // poll pauseAll flag every 100
static volatile boolean ping_anyActions = false;
static Map<Thread, Object> ping_actions = newWeakHashMap();
static ThreadLocal<Boolean> ping_isCleanUpThread = new ThreadLocal();

// ignore pingSource if not PingV3
static boolean ping(PingSource pingSource) { return ping(); }

// always returns true
static boolean ping() {
  //ifdef useNewPing
  newPing();
  //endifdef
  if (ping_pauseAll || ping_anyActions) ping_impl(true /* XXX */);
  //ifndef LeanMode ping_impl(); endifndef
  return true;
}

// returns true when it slept
static boolean ping_impl(boolean okInCleanUp) { try {
  if (ping_pauseAll && !isAWTThread()) {
    do
      Thread.sleep(ping_sleep);
    while (ping_pauseAll);
    return true;
  }
  
  if (ping_anyActions) { // don't allow sharing ping_actions
    if (!okInCleanUp && !isTrue(ping_isCleanUpThread.get()))
      failIfUnlicensed();
    Object action = null;
    synchronized(ping_actions) {
      if (!ping_actions.isEmpty()) {
        action = ping_actions.get(currentThread());
        if (action instanceof Runnable)
          ping_actions.remove(currentThread());
        if (ping_actions.isEmpty()) ping_anyActions = false;
      }
    }
    
    if (action instanceof Runnable)
      ((Runnable) action).run();
    else if (eq(action, "cancelled"))
      throw fail("Thread cancelled.");
  }

  return false;
} catch (Exception __e) { throw rethrow(__e); } }




static Object endMarker() {
  return iteratorFromFunction_endMarker;
}


static class mapI_if1_It<A, B> extends IterableIterator<B> {
  IF1<A, B> f;
  Iterator<A> i;
  
  mapI_if1_It() {}
  mapI_if1_It(IF1<A, B> f, Iterator<A> i) {
  this.i = i;
  this.f = f;}
  
  public boolean hasNext() {
    return i.hasNext();
  }
  
  public B next() {
    return f.get(i.next());
  }
  
  public String toString() {
    return formatFunctionCall("mapI_if1", f, i);
  }
}

static <A, B> IterableIterator<B> mapI_if1(IF1<A, B> f, Iterable<A> i) {
  return new mapI_if1_It(f, i.iterator());
}



static <A, B> IterableIterator<B> mapI_if1(Iterable<A> i, IF1<A, B> f) {
  return mapI_if1(f, i);
}


static Iterator emptyIterator() {
  return Collections.emptyIterator();
}


// custom mainClass only works with hotwire_here
static Class<?> hotwire(String src) { return hotwire(src, __1 -> mainClassNameForClassLoader(__1)); }
static Class<?> hotwire(String src, IF1<ClassLoader, String> calculateMainClass) {
  assertFalse(_inCore());
  Class j = getJavaX();
  if (isAndroid()) {
    synchronized(j) { // hopefully this goes well...
      List<File> libraries = new ArrayList<File>();
      File srcDir = (File) call(j, "transpileMain", src, libraries);
      if (srcDir == null)
        throw fail("transpileMain returned null (src=" + quote(src) + ")");
    
      Object androidContext = get(j, "androidContext");
      return (Class) call(j, "loadx2android", srcDir, src);
    }
  } else {
    
    
    Class c =  (Class) (call(j, "hotwire", src));
    hotwire_copyOver(c);
    return c;
    
  }
}


static <A> A callMain(A c, String... args) {
  callOpt(c, "main", new Object[] {args});
  return c;
}

static void callMain() {
  callMain(mc());
}


static String shortClassName_dropNumberPrefix(Object o) {
  return dropNumberPrefix(shortClassName(o));
}



static Map<Class, ArrayList<Method>> callF_cache = newDangerousWeakHashMap();



  static <A> A callF(F0<A> f) {
    return f == null ? null : f.get();
  }



  static <A, B> B callF(F1<A, B> f, A a) {
    return f == null ? null : f.get(a);
  }



  static <A> A callF(IF0<A> f) {
    return f == null ? null : f.get();
  }



  static <A, B> B callF(IF1<A, B> f, A a) {
    return f == null ? null : f.get(a);
  }


static <A, B> B callF(A a, IF1<A, B> f) {
  return f == null ? null : f.get(a);
}




  static <A, B, C> C callF(IF2<A, B, C> f, A a, B b) {
    return f == null ? null : f.get(a, b);
  }



  static <A> void callF(VF1<A> f, A a) {
    if (f != null) f.get(a);
  }


static <A> void callF(A a, IVF1<A> f) {
  if (f != null) f.get(a);
}

static <A> void callF(IVF1<A> f, A a) {
  if (f != null) f.get(a);
}


static Object callF(Runnable r) { { if (r != null) r.run(); } return null; }


static Object callF(Object f, Object... args) {
  
    
  return safeCallF(f, args);
}

static Object safeCallF(Object f, Object... args) {
  if (f instanceof Runnable) {
    ((Runnable) f).run();
    return null;
  }
  if (f == null) return null;
  
  Class c = f.getClass();
  ArrayList<Method> methods;
  synchronized(callF_cache) {
    methods = callF_cache.get(c);
    if (methods == null)
      methods = callF_makeCache(c);
  }
  
  int n = l(methods);
  if (n == 0) {
    
    
    if (f instanceof String)
      throw fail("Legacy call: " + f);
    
    throw fail("No get method in " + getClassName(c));
  }
  if (n == 1) return invokeMethod(methods.get(0), f, args);
  for (int i = 0; i < n; i++) {
    Method m = methods.get(i);
    if (call_checkArgs(m, args, false))
      return invokeMethod(m, f, args);
  }
  throw fail("No matching get method in " + getClassName(c));
}

// used internally
static ArrayList<Method> callF_makeCache(Class c) {
  ArrayList<Method> l = new ArrayList();
  Class _c = c;
  do {
    for (Method m : _c.getDeclaredMethods())
      if (m.getName().equals("get")) {
        makeAccessible(m);
        l.add(m);
      }
    if (!l.isEmpty()) break;
    _c = _c.getSuperclass();
  } while (_c != null);
  callF_cache.put(c, l);
  return l;
}





static <A> IterableIterator<A> iteratorFromFunction_f0(final F0<A> f) {
  class IFF2 extends IterableIterator<A> {
    A a;
    boolean done = false;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      return _a;
    }
    
    void getNext() {
      if (done || a != null) return;
      a = f.get();
      done = a == null;
    }
  };
  return new IFF2();
}


static <A> IterableIterator<A> iteratorFromFunction_if0(final IF0<A> f) {
  class IFF2 extends IterableIterator<A> {
    A a;
    boolean done = false;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      return _a;
    }
    
    void getNext() {
      if (done || a != null) return;
      a = f.get();
      done = a == null;
    }
  };
  return new IFF2();
}


static java.awt.Color awtColor(String hex) {
  byte[] b = bytesFromHex(dropPrefix("#", hex));
  return new Color(ubyteToInt(b[0]), ubyteToInt(b[1]), ubyteToInt(b[2]));
}


// binary legacy syntax
static String formatFunctionCall(String fname, Object... args) {
  return formatFunctionCall((Object) fname, args);
}
  
static String formatFunctionCall(Object fname, Object... args) {
  return fname + "(" + joinWithComma(allToString(args)) + ")";
}

static String formatFunctionCall(String fname, Iterable args) {
  return formatFunctionCall((Object) fname, args);
}

static String formatFunctionCall(Object fname, Iterable args) {
  return formatFunctionCall(fname, toObjectArray(args));
}




// requires ugly casting when used (O -> A)
static Object iteratorFromFunction_endMarker = new Object();

// f: func -> A | endMarker
static <A> IterableIterator<A> iteratorFromFunction_withEndMarker(final Object f) {
  class IFF extends IterableIterator<A> {
    A a;
    boolean have, done;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      have = false;
      return _a;
    }
    
    void getNext() {
      if (done || have) return;
      Object o = callF(f);
      if (o == iteratorFromFunction_endMarker)
        { done = true; return; }
      a = (A) o;
      have = true;
    }
  };
  return new IFF();
}

// optimized version for F0 argument; TODO: do same for IF0
static <A> IterableIterator<A> iteratorFromFunction_withEndMarker(final F0 f) {
  return iteratorFromFunction_withEndMarker_f0(f);
}


static Map<Class, Constructor> nuEmptyObject_cache = newDangerousWeakHashMap();

static <A> A nuEmptyObject(Class<A> c) { try {
  Constructor ctr;
  
  synchronized(nuEmptyObject_cache) {
    ctr = nuEmptyObject_cache.get(c);
    if (ctr == null) {
      nuEmptyObject_cache.put(c, ctr = nuEmptyObject_findConstructor(c));
      makeAccessible(ctr);
    }
  }

  try {
    return (A) ctr.newInstance();
  } catch (InstantiationException e) {
    if (empty(e.getMessage()))
      if ((c.getModifiers() & Modifier.ABSTRACT) != 0)
        throw fail("Can't instantiate abstract class " + className(c), e);
      else
        throw fail("Can't instantiate " + className(c), e);  
    else throw rethrow(e);
  }
} catch (Exception __e) { throw rethrow(__e); } }

static Constructor nuEmptyObject_findConstructor(Class c) {
  for (Constructor m : getDeclaredConstructors_cached(c))
    if (m.getParameterTypes().length == 0)
      return m;
  throw fail("No default constructor declared in " + c.getName());
}



static volatile StringBuffer local_log = new StringBuffer(); // not redirected




static boolean printAlsoToSystemOut = true;

static volatile Appendable print_log = local_log; // might be redirected, e.g. to main bot

// in bytes - will cut to half that
static volatile int print_log_max = 1024*1024;
static volatile int local_log_max = 100*1024;

static boolean print_silent = false; // total mute if set

static Object print_byThread_lock = new Object();
static volatile ThreadLocal<Object> print_byThread; // special handling by thread - prefers F1<S, Bool>
static volatile Object print_allThreads;
static volatile Object print_preprocess;

static void print() {
  print("");
}

static <A> A print(String s, A o) {
  print(combinePrintParameters(s, o));
  return o;
}

// slightly overblown signature to return original object...
static <A> A print(A o) {
  ping_okInCleanUp();
  if (print_silent) return o;
  String s = o + "\n";
  print_noNewLine(s);
  return o;
}

static void print_noNewLine(String s) {
  
  try {
    Object f = getThreadLocal(print_byThread_dontCreate());
    if (f == null) f = print_allThreads;
      if (f != null)
        // We do need the general callF machinery here as print_byThread is sometimes shared between modules
        if (isFalse(
          
            f instanceof F1 ? ((F1) f).get(s) :
          
          callF(f, s))) return;
  } catch (Throwable e) {
    System.out.println(getStackTrace(e));
  }
  

  print_raw(s);
}

static void print_raw(String s) {
  
  if (print_preprocess != null) s = (String) callF(print_preprocess, s);
  s = fixNewLines(s);
  
  Appendable loc = local_log;
  Appendable buf = print_log;
  int loc_max = print_log_max;
  if (buf != loc && buf != null) {
    print_append(buf, s, print_log_max);
    loc_max = local_log_max;
  }
  if (loc != null) 
    print_append(loc, s, loc_max);
  
  
  if (printAlsoToSystemOut)
    System.out.print(s);
  
  
  vmBus_send("printed", mc(), s);
  
}

static void print_autoRotate() {
  
}


// Use like this: renderVars(+x, +y)
// Or like this: renderVars("bla", +x, +y)
static String renderVars_str(Object... params) {
  List<String> l = new ArrayList();
  int i = 0;
  if (odd(l(params))) {
    l.add(strOrNull(first(params)));
    ++i;
  }
  for (; i+1 < l(params); i += 2)
    l.add(params[i] + "=" + params[i+1]);
  return trim(joinWithComma(l));
}


static String getClassName(Object o) {
  return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}


static void vmBus_send(String msg, Object... args) {
  Object arg = vmBus_wrapArgs(args);
  pcallFAll_minimalExceptionHandling(vm_busListeners_live(), msg, arg);
  pcallFAll_minimalExceptionHandling(vm_busListenersByMessage_live().get(msg), msg, arg);
}

static void vmBus_send(String msg) {
  vmBus_send(msg, (Object) null);
}


static String formatWithThousands(long l) {
  return formatWithThousandsSeparator(l);
}


static String plural(String s) {
  return getPlural(s);
}


static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return c == null ? "null" : new String(c);
}

static String str(char[] c, int offset, int count) {
  return new String(c, offset, count);
}


static double fraction(double d) {
  return d % 1;
}


static String n_fancy2(long l, String singular, String plural) {
  return formatWithThousandsSeparator(l) + " " + trim(l == 1 ? singular : plural);
}

static String n_fancy2(Collection l, String singular, String plural) {
  return n_fancy2(l(l), singular, plural);
}

static String n_fancy2(Map m, String singular, String plural) {
  return n_fancy2(l(m), singular, plural);
}

static String n_fancy2(Object[] a, String singular, String plural) {
  return n_fancy2(l(a), singular, plural);
}




static IterableIterator emptyIterableIterator_instance = new IterableIterator() {
  public Object next() { throw fail(); }
  public boolean hasNext() { return false; }
};

static <A> IterableIterator<A> emptyIterableIterator() {
  return emptyIterableIterator_instance; 
}


static <A, B> Map<A, B> newWeakHashMap() {
  return _registerWeakMap(synchroMap(new WeakHashMap()));
}


static void newPing() {
  var tl = newPing_actionTL();
  Runnable action = tl == null ? null : tl.get();
  { if (action != null) action.run(); }
}


// TODO: test if android complains about this
static boolean isAWTThread() {
  if (isAndroid()) return false;
  if (isHeadless()) return false;
  return isAWTThread_awt();
}

static boolean isAWTThread_awt() {
  return SwingUtilities.isEventDispatchThread();
}


static boolean isTrue(Object o) {
  if (o instanceof Boolean)
    return ((Boolean) o).booleanValue();
  if (o == null) return false;
  if (o instanceof ThreadLocal) // TODO: remove this
    return isTrue(((ThreadLocal) o).get());
  throw fail(getClassName(o));
}

static boolean isTrue(Boolean b) {
  return b != null && b.booleanValue();
}


static void failIfUnlicensed() {
  assertTrue("license off", licensed());
}


static Thread currentThread() {
  return Thread.currentThread();
}


static boolean eq(Object a, Object b) {
  return a == b || a != null && b != null && a.equals(b);
}


// a little kludge for stuff like eq(symbol, "$X")
static boolean eq(Symbol a, String b) {
  return eq(str(a), b);
}



static String mainClassNameForClassLoader(ClassLoader cl) {
  return or((String) callOpt(cl, "mainClassName"), "main");
}


static void assertFalse(Object o) {
  if (!(eq(o, false) /*|| isFalse(pcallF(o))*/))
    throw fail(str(o));
}
  
static boolean assertFalse(boolean b) {
  if (b) throw fail("oops");
  return b;
}

static boolean assertFalse(String msg, boolean b) {
  if (b) throw fail(msg);
  return b;
}



static boolean _inCore() {
  return false;
}


static Class __javax;

static Class getJavaX() { try {
  
  return __javax;
} catch (Exception __e) { throw rethrow(__e); } }

static void __setJavaX(Class j) {
  __javax = j;
  _onJavaXSet();
}


static int isAndroid_flag;

static boolean isAndroid() {
  if (isAndroid_flag == 0)
    isAndroid_flag = System.getProperty("java.vendor").toLowerCase().indexOf("android") >= 0 ? 1 : -1;
  return isAndroid_flag > 0;
}



static Object call(Object o) {
  return callF(o);
}

// varargs assignment fixer for a single string array argument
static Object call(Object o, String method, String[] arg) {
  return call(o, method, new Object[] {arg});
}

static Object call(Object o, String method, Object... args) {
  //ret call_cached(o, method, args);
  return call_withVarargs(o, method, args);
}


static String quote(Object o) {
  if (o == null) return "null";
  return quote(str(o));
}

static String quote(String s) {
  if (s == null) return "null";
  StringBuilder out = new StringBuilder((int) (l(s)*1.5+2));
  quote_impl(s, out);
  return out.toString();
}
  
static void quote_impl(String s, StringBuilder out) {
  out.append('"');
  int l = s.length();
  for (int i = 0; i < l; i++) {
    char c = s.charAt(i);
    if (c == '\\' || c == '"')
      out.append('\\').append(c);
    else if (c == '\r')
      out.append("\\r");
    else if (c == '\n')
      out.append("\\n");
    else if (c == '\t')
      out.append("\\t");
    else if (c == '\0')
      out.append("\\0");
    else
      out.append(c);
  }
  out.append('"');
}


static List hotwire_copyOver_after = synchroList();

static void hotwire_copyOver(Class c) {
  // TODO: make a mechanism for making such "inheritable" fields
  for (String field : ll("print_log", "print_silent", "androidContext", "_userHome"))
    setOptIfNotNull(c, field, getOpt(mc(), field));
    
  
  
  setOptIfNotNull(c, "mainBot" , getMainBot());
  setOpt(c, "creator_class" , new WeakReference(mc()));
  pcallFAll(hotwire_copyOver_after, c);
}


static Object callOpt(Object o) {
  return callF(o);
}

static Object callOpt(Object o, String method, Object... args) {
  return callOpt_withVarargs(o, method, args);
}


static Class mc() {
  return main.class;
}


static String dropNumberPrefix(String s) {
  return dropFirst(s, indexOfNonDigit(s));
}


static String shortClassName(Object o) {
  if (o == null) return null;
  Class c = o instanceof Class ? (Class) o : o.getClass();
  String name = c.getName();
  return shortenClassName(name);
}


static <A, B> Map<A, B> newDangerousWeakHashMap() {
  return _registerDangerousWeakMap(synchroMap(new WeakHashMap()));
}

// initFunction: voidfunc(Map) - is called initially, and after clearing the map
static <A, B> Map<A, B> newDangerousWeakHashMap(Object initFunction) {
  return _registerDangerousWeakMap(synchroMap(new WeakHashMap()), initFunction);
}


static Object invokeMethod(Method m, Object o, Object... args) { try {
  try {
    return m.invoke(o, args);
  } catch (InvocationTargetException e) {
    throw rethrow(getExceptionCause(e));
  } catch (IllegalArgumentException e) {
    throw new IllegalArgumentException(e.getMessage() + " - was calling: " + m + ", args: " + joinWithSpace(classNames(args)));
  }
} catch (Exception __e) { throw rethrow(__e); } }


static boolean call_checkArgs(Method m, Object[] args, boolean debug) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != l(args)) {
    if (debug)
      print("Bad parameter length: " + args.length + " vs " + types.length);
    return false;
  }
  for (int i = 0; i < types.length; i++) {
    Object arg = args[i];
    if (!(arg == null ? !types[i].isPrimitive()
      : isInstanceX(types[i], arg))) {
      if (debug)
        print("Bad parameter " + i + ": " + arg + " vs " + types[i]);
      return false;
    }
  }
  return true;
}


static byte[] bytesFromHex(String s) {
  return hexToBytes(s);
}


static String dropPrefix(String prefix, String s) {
  return s == null ? null : s.startsWith(prefix) ? s.substring(l(prefix)) : s;
}


static int ubyteToInt(byte b) {
  return b & 0x0FF;
}

static int ubyteToInt(char c) {
  return c & 0x0FF;
}


static <A> String joinWithComma(Iterable<A> c) {
  return join(", ", c);
}

static String joinWithComma(Object... c) {
  return join(", ", c);
}

static String joinWithComma(String... c) {
  return join(", ", c);
}


static String joinWithComma(Pair p) {
  return p == null ? "" : joinWithComma(str(p.a), str(p.b));
}



static List<String> allToString(Iterable c) {
  List<String> l = new ArrayList();
  for (Object o : unnull(c)) l.add(str(o));
  return l;
}

static List<String> allToString(Object[] c) {
  List<String> l = new ArrayList();
  for (Object o : unnull(c)) l.add(str(o));
  return l;
}


// binary legacy signature
static Object[] toObjectArray(Collection c) {
  return toObjectArray((Iterable) c);
}

static Object[] toObjectArray(Iterable c) {
  List l = asList(c);
  return l.toArray(new Object[l.size()]);
}





static AutoCloseable tempInterceptPrintIfNotIntercepted(F1<String, Boolean> f) {
  return print_byThread().get() == null ? tempInterceptPrint(f) : null;
}


static <A> IterableIterator<A> iteratorFromFunction_withEndMarker_f0(final F0<A> f) {
  class IFF2 extends IterableIterator<A> {
    A a;
    boolean have, done;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      have = false;
      return _a;
    }
    
    void getNext() {
      if (done || have) return;
      Object o = f.get();
      if (o == iteratorFromFunction_endMarker)
        { done = true; return; }
      a = (A) o;
      have = true;
    }
  };
  return new IFF2();
}


static String className(Object o) {
  return getClassName(o);
}




// TODO: convert to regularly cleared normal map
static Map<Class, Constructor[]> getDeclaredConstructors_cached_cache = newDangerousWeakHashMap();

static Constructor[] getDeclaredConstructors_cached(Class c) {
  Constructor[] ctors;
  synchronized(getDeclaredConstructors_cached_cache) {
    ctors = getDeclaredConstructors_cached_cache.get(c);
    if (ctors == null) {
      getDeclaredConstructors_cached_cache.put(c, ctors = c.getDeclaredConstructors());
      for (var ctor : ctors)
        makeAccessible(ctor);
    }
  }
  return ctors;
}


static String combinePrintParameters(String s, Object o) {
  return (endsWithLetterOrDigit(s) ? s + ": " : s) + o;
}


static void ping_okInCleanUp() {


  if (ping_pauseAll || ping_anyActions)
    ping_impl(true);


}


// this syntax should be removed...
static Object getThreadLocal(Object o, String name) {
  ThreadLocal t =  (ThreadLocal) (getOpt(o, name));
  return t != null ? t.get() : null;
}

static <A> A getThreadLocal(ThreadLocal<A> tl) {
  return tl == null ? null : tl.get();
}

static <A> A getThreadLocal(ThreadLocal<A> tl, A defaultValue) {
  return or(getThreadLocal(tl), defaultValue);
}


static ThreadLocal<Object> print_byThread_dontCreate() {
  return print_byThread;
}


static boolean isFalse(Object o) {
  return eq(false, o);
}


static String getStackTrace(Throwable throwable) {
  lastException(throwable);
  return getStackTrace_noRecord(throwable);
}

static String getStackTrace_noRecord(Throwable throwable) {
  StringWriter writer = new StringWriter();
  throwable.printStackTrace(new PrintWriter(writer));
  return hideCredentials(writer.toString());
}

static String getStackTrace() {
  return getStackTrace_noRecord(new Throwable());
}

static String getStackTrace(String msg) {
  return getStackTrace_noRecord(new Throwable(msg));
}


static String fixNewLines(String s) {
  int i = indexOf(s, '\r');
  if (i < 0) return s;
  int l = s.length();
  StringBuilder out = new StringBuilder(l);
  out.append(s, 0, i);
  for (; i < l; i++) {
    char c = s.charAt(i);
    if (c != '\r')
      out.append(c);
    else {
      out.append('\n');
      if (i+1 < l && s.charAt(i+1) == '\n') ++i;
    }
  }
  return out.toString();
}


static void print_append(Appendable buf, String s, int max) { try {
  synchronized(buf) {
    buf.append(s);
    if (buf instanceof StringBuffer)
      rotateStringBuffer(((StringBuffer) buf), max);
    else if (buf instanceof StringBuilder)
      rotateStringBuilder(((StringBuilder) buf), max);
  }
} catch (Exception __e) { throw rethrow(__e); } }


static boolean odd(int i) {
  return (i & 1) != 0;
}

static boolean odd(long i) {
  return (i & 1) != 0;
}

static boolean odd(BigInteger i) { return odd(toInt(i)); }


static String strOrNull(Object o) {
  return o == null ? null : str(o);
}



static Object first(Object list) {
  return first((Iterable) list);
}


static <A> A first(List<A> list) {
  return empty(list) ? null : list.get(0);
}

static <A> A first(A[] bla) {
  return bla == null || bla.length == 0 ? null : bla[0];
}

static <A, B> Pair<A, B> first(Map<A, B> map) {
  return mapEntryToPair(first(entrySet(map)));
}

static <A, B> Pair<A, B> first(MultiMap<A, B> mm) {
  if (mm == null) return null;
  var e = first(mm.data.entrySet());
  if (e == null) return null;
  return pair(e.getKey(), first(e.getValue()));
}


static <A> A first(IterableIterator<A> i) {
  return first((Iterator<A>) i);
}


static <A> A first(Iterator<A> i) {
  return i == null || !i.hasNext() ? null : i.next();
}

static <A> A first(Iterable<A> i) {
  if (i == null) return null;
  Iterator<A> it = i.iterator();
  return it.hasNext() ? it.next() : null;
}

static Character first(String s) { return empty(s) ? null : s.charAt(0); }
static Character first(CharSequence s) { return empty(s) ? null : s.charAt(0); }


static <A, B> A first(Pair<A, B> p) {
  return p == null ? null : p.a;
}




static Byte first(byte[] l) { return empty(l) ? null : l[0]; }
static Double first(double[] l) { return empty(l) ? null : l[0]; }


static int first(IntBuffer buf) {
  return buf.get(0);
}



static byte first(ByteBuffer buf) {
  return buf.get(0);
}


static <A> A first(A[] l, IF1<A, Boolean> pred) {
  return firstThat(l, pred);
}

static <A> A first(Iterable<A> l, IF1<A, Boolean> pred) {
  return firstThat(l, pred);
}

static <A> A first(IF1<A, Boolean> pred, Iterable<A> l) {
  return firstThat(pred, l);
}


static <A> A first(AppendableChain<A> a) {
  return a == null ? null : a.element;
}




static String trim(String s) { return s == null ? null : s.trim(); }
static String trim(StringBuilder buf) { return buf.toString().trim(); }
static String trim(StringBuffer buf) { return buf.toString().trim(); }


static Object vmBus_wrapArgs(Object... args) {
  return empty(args) ? null
    : l(args) == 1 ? args[0]
    : args;
}


static void pcallFAll_minimalExceptionHandling(Collection l, Object... args) {
  if (l != null) for  (Object f : cloneList(l)) { ping(); pcallF_minimalExceptionHandling(f, args); }
}

static void pcallFAll_minimalExceptionHandling(Iterator it, Object... args) {
  while  (it.hasNext()) { ping(); pcallF_minimalExceptionHandling(it.next(), args); }
}


static Set vm_busListeners_live_cache;
static Set vm_busListeners_live() { if (vm_busListeners_live_cache == null) vm_busListeners_live_cache = vm_busListeners_live_load(); return vm_busListeners_live_cache;}

static Set vm_busListeners_live_load() {
  return vm_generalIdentityHashSet("busListeners");
}


static Map<String, Set> vm_busListenersByMessage_live_cache;
static Map<String, Set> vm_busListenersByMessage_live() { if (vm_busListenersByMessage_live_cache == null) vm_busListenersByMessage_live_cache = vm_busListenersByMessage_live_load(); return vm_busListenersByMessage_live_cache;}

static Map<String, Set> vm_busListenersByMessage_live_load() {
  return vm_generalHashMap("busListenersByMessage");
}




static String formatWithThousandsSeparator(long l) {
  return NumberFormat.getInstance(new Locale("en_US")).format(l);
}


static Set<String> getPlural_specials = litciset("sheep", "fish");

static String getPlural(String s) {
  if (contains(getPlural_specials, s)) return s;
  if (ewic(s, "y")) return dropSuffixIgnoreCase("y", s) + "ies";
  if (ewicOneOf(s, "ss", "ch")) return s + "es";
  if (ewic(s, "s")) return s;
  return s + "s";
}


static List _registerWeakMap_preList;

static <A> A _registerWeakMap(A map) {
  if (javax() == null) {
    // We're in class init
    if (_registerWeakMap_preList == null) _registerWeakMap_preList = synchroList();
    _registerWeakMap_preList.add(map);
    return map;
  }
  
  try {
    call(javax(), "_registerWeakMap", map);
  } catch (Throwable e) {
    printException(e);
    print("Upgrade JavaX!!");
  }
  return map;
}

static void _onLoad_registerWeakMap() {
  assertNotNull(javax());
  if (_registerWeakMap_preList == null) return;
  for (Object o : _registerWeakMap_preList)
    _registerWeakMap(o);
  _registerWeakMap_preList = null;
}


static Map synchroMap() {
  return synchroHashMap();
}

static <A, B> Map<A, B> synchroMap(Map<A, B> map) {
  
  
    return Collections.synchronizedMap(map);
  
}


static x30_pkg.x30_util.BetterThreadLocal<Runnable> newPing_actionTL;

static x30_pkg.x30_util.BetterThreadLocal<Runnable> newPing_actionTL() {
  if (newPing_actionTL == null)
    newPing_actionTL = vm_generalMap_getOrCreate("newPing_actionTL",
      () -> {
        Runnable value =  (Runnable) (callF_gen(vm_generalMap_get("newPing_valueForNewThread")));
        var tl = new x30_pkg.x30_util.BetterThreadLocal<Runnable>();
        tl.set(value);
        return tl;
      });
  return newPing_actionTL;
}



static Boolean isHeadless_cache;

static boolean isHeadless() {
  if (isHeadless_cache != null) return isHeadless_cache;
  if (isAndroid()) return isHeadless_cache = true;
  if (GraphicsEnvironment.isHeadless()) return isHeadless_cache = true;
  
  // Also check if AWT actually works.
  // If DISPLAY variable is set but no X server up, this will notice.
  
  try {
    SwingUtilities.isEventDispatchThread();
    return isHeadless_cache = false;
  } catch (Throwable e) { return isHeadless_cache = true; }
}


static void assertTrue(Object o) {
  if (!(eq(o, true) /*|| isTrue(pcallF(o))*/))
    throw fail(str(o));
}
  
static boolean assertTrue(String msg, boolean b) {
  if (!b)
    throw fail(msg);
  return b;
}

static boolean assertTrue(boolean b) {
  if (!b)
    throw fail("oops");
  return b;
}

static boolean assertTrue(Scorer scorer, boolean b) {
  scorer.add(b);
  return b;
}


static volatile boolean licensed_yes = true;

static boolean licensed() {
  if (!licensed_yes) return false;
  ping_okInCleanUp();
  return true;
}

static void licensed_off() {
  licensed_yes = false;
}


static <A> A or(A a, A b) {
  return a != null ? a : b;
}


static void _onJavaXSet() {}


static Object call_withVarargs(Object o, String methodName, Object... args) { try {
  if (o == null) return null;
  
  if (o instanceof Class) {
    Class c = (Class) o;
    _MethodCache cache = callOpt_getCache(c);
    
    Method me = cache.findStaticMethod(methodName, args);
    if (me != null)
      return invokeMethod(me, null, args);
      
    // try varargs
    List<Method> methods = cache.cache.get(methodName);
    if (methods != null) methodSearch: for (Method m : methods) {
      { if (!(m.isVarArgs())) continue; }
      { if (!(isStaticMethod(m))) continue; }
      Object[] newArgs = massageArgsForVarArgsCall(m, args);
      if (newArgs != null)
        return invokeMethod(m, null, newArgs);
    }
    
    throw fail("Method " + c.getName() + "." + methodName + "(" + formatArgumentClasses(args) + ") not found");
  } else {
    Class c = o.getClass();
    _MethodCache cache = callOpt_getCache(c);

    Method me = cache.findMethod(methodName, args);
    if (me != null)
      return invokeMethod(me, o, args);
      
    // try varargs
    List<Method> methods = cache.cache.get(methodName);
    if (methods != null) methodSearch: for (Method m : methods) {
      { if (!(m.isVarArgs())) continue; }
      Object[] newArgs = massageArgsForVarArgsCall(m, args);
      if (newArgs != null)
        return invokeMethod(m, o, newArgs);
    }
    
    throw fail("Method " + c.getName() + "." + methodName + "(" + formatArgumentClasses(args) + ") not found");
  }
} catch (Exception __e) { throw rethrow(__e); } }


static <A> List<A> synchroList() {
  return synchroList(new ArrayList<A>());
}

static <A> List<A> synchroList(List<A> l) {
  
  
    return Collections.synchronizedList(l);
  
}



static <A> List<A> ll(A... a) {
  ArrayList l = new ArrayList(a.length);
  if (a != null) for (A x : a) l.add(x);
  return l;
}


static void setOptIfNotNull(Object o, String field, Object value) {
  if (value != null) setOpt(o, field, value);
}


static Object getOpt(Object o, String field) {
  return getOpt_cached(o, field);
}

static Object getOpt(String field, Object o) {
  return getOpt_cached(o, field);
}

static Object getOpt_raw(Object o, String field) { try {
  Field f = getOpt_findField(o.getClass(), field);
  if (f == null) return null;
  makeAccessible(f);
  return f.get(o);
} catch (Exception __e) { throw rethrow(__e); } }

// access of static fields is not yet optimized
static Object getOpt(Class c, String field) { try {
  if (c == null) return null;
  Field f = getOpt_findStaticField(c, field);
  if (f == null) return null;
  makeAccessible(f);
  return f.get(null);
} catch (Exception __e) { throw rethrow(__e); } }

static Field getOpt_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}



static Object mainBot;

static Object getMainBot() {
  return mainBot;
}


static Field setOpt_findField(Class c, String field) {
  HashMap<String, Field> map;
  synchronized(getOpt_cache) {
    map = getOpt_cache.get(c);
    if (map == null)
      map = getOpt_makeCache(c);
  }
  return map.get(field);
}

static void setOpt(Object o, String field, Object value) { try {
  if (o == null) return;
  
  
  
  Class c = o.getClass();
  HashMap<String, Field> map;
  
  if (getOpt_cache == null)
    map = getOpt_makeCache(c); // in class init
  else synchronized(getOpt_cache) {
    map = getOpt_cache.get(c);
    if (map == null)
      map = getOpt_makeCache(c);
  }
  
  if (map == getOpt_special) {
    if (o instanceof Class) {
      setOpt((Class) o, field, value);
      return;
    }
    
    // It's probably a subclass of Map. Use raw method. TODO: huh?
    setOpt_raw(o, field, value);
    return;
  }
  
  Field f = map.get(field);
  
  if (f != null)
    { smartSet(f, o, value); return; } // possible improvement: skip setAccessible
  
    if (o instanceof DynamicObject)
      { setDyn(((DynamicObject) o), field, value); return; }
  
  if (o instanceof IMeta)
    setDyn(((IMeta) o), field, value);
} catch (Exception __e) { throw rethrow(__e); } }

static void setOpt(Class c, String field, Object value) {
  if (c == null) return;
  try {
    Field f = setOpt_findStaticField(c, field); // TODO: optimize
    if (f != null)
      smartSet(f, null, value);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}
  
static Field setOpt_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0) {
        makeAccessible(f);
        return f;
      }
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}


static void pcallFAll(Collection l, Object... args) {
  if (l != null) for (Object f : cloneList(l)) pcallF(f, args);
}

static void pcallFAll(Iterator it, Object... args) {
  while (it.hasNext()) pcallF(it.next(), args);
}


static Object callOpt_withVarargs(Object o, String method, Object... args) { try {
  if (o == null) return null;
  
  if (o instanceof Class) {
    Class c = (Class) o;
    _MethodCache cache = callOpt_getCache(c);
    
    Method me = cache.findMethod(method, args);
    if (me == null) {
      // TODO: varargs
      return null;
    }
    if ((me.getModifiers() & Modifier.STATIC) == 0)
      return null;
    return invokeMethod(me, null, args);
  } else {
    Class c = o.getClass();
    _MethodCache cache = callOpt_getCache(c);

    Method me = cache.findMethod(method, args);
    if (me != null)
      return invokeMethod(me, o, args);
      
    // try varargs
    List<Method> methods = cache.cache.get(method);
    if (methods != null) methodSearch: for (Method m : methods) {
      { if (!(m.isVarArgs())) continue; }
      Object[] newArgs = massageArgsForVarArgsCall(m, args);
      if (newArgs != null)
        return invokeMethod(m, o, newArgs);
    }
    
    return null;
  }
} catch (Exception __e) { throw rethrow(__e); } }


static String[] dropFirst(int n, String[] a) {
  return drop(n, a);
}

static String[] dropFirst(String[] a) {
  return drop(1, a);
}

static Object[] dropFirst(Object[] a) {
  return drop(1, a);
}

static <A> List<A> dropFirst(List<A> l) {
  return dropFirst(1, l);
}

static <A> List<A> dropFirst(int n, Iterable<A> i) { return dropFirst(n, toList(i)); }
static <A> List<A> dropFirst(Iterable<A> i) { return dropFirst(toList(i)); }

static <A> List<A> dropFirst(int n, List<A> l) {
  return n <= 0 ? l : new ArrayList(l.subList(Math.min(n, l.size()), l.size()));
}

static <A> List<A> dropFirst(List<A> l, int n) {
  return dropFirst(n, l);
}

static String dropFirst(int n, String s) { return substring(s, n); }
static String dropFirst(String s, int n) { return substring(s, n); }
static String dropFirst(String s) { return substring(s, 1); }


static <A> Chain<A> dropFirst(Chain<A> c) {
  return c == null ? null : c.next;
}



static int indexOfNonDigit(String s) {
  int n = l(s);
  for (int i = 0; i < n; i++)
    if (!isDigit(s.charAt(i)))
      return i;
  return -1;
}


static String shortenClassName(String name) {
  if (name == null) return null;
  int i = lastIndexOf(name, "$");
  if (i < 0) i = lastIndexOf(name, ".");
  return i < 0 ? name : substring(name, i+1);
}


static List<Pair> _registerDangerousWeakMap_preList;

static <A> A _registerDangerousWeakMap(A map) {
  return _registerDangerousWeakMap(map, null);
}

static <A> A _registerDangerousWeakMap(A map, Object init) {
  
  callF(init, map);
  
  if (init instanceof String) {
    final String f =  (String) init;
    init = new VF1<Map>() { public void get(Map map) { try {  callMC(f, map) ; } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "callMC(f, map)"; }};
  }
    
  if (javax() == null) {
    // We're in class init
    if (_registerDangerousWeakMap_preList == null) _registerDangerousWeakMap_preList = synchroList();
    _registerDangerousWeakMap_preList.add(pair(map, init));
    return map;
  }
  
  call(javax(), "_registerDangerousWeakMap", map, init);
  
  return map;
}

static void _onLoad_registerDangerousWeakMap() {
  
  assertNotNull(javax());
  if (_registerDangerousWeakMap_preList == null) return;
  for (Pair p : _registerDangerousWeakMap_preList)
    _registerDangerousWeakMap(p.a, p.b);
  _registerDangerousWeakMap_preList = null;
  
}


static Throwable getExceptionCause(Throwable e) {
  Throwable c = e.getCause();
  return c != null ? c : e;
}


static String joinWithSpace(Iterable c) {
  return join(" ", c);
}

static String joinWithSpace(Object... c) {
  return join(" ", c);
}



static List<String> classNames(Collection l) {
  return getClassNames(l);
}

static List<String> classNames(Object[] l) {
  return getClassNames(asList(l));
}


static boolean isInstanceX(Class type, Object arg) {
  if (type == boolean.class) return arg instanceof Boolean;
  if (type == int.class) return arg instanceof Integer;
  if (type == long.class) return arg instanceof Long;
  if (type == float.class) return arg instanceof Float;
  if (type == short.class) return arg instanceof Short;
  if (type == char.class) return arg instanceof Character;
  if (type == byte.class) return arg instanceof Byte;
  if (type == double.class) return arg instanceof Double;
  return type.isInstance(arg);
}


static byte[] hexToBytes(String s) {
  if (odd(l(s))) throw fail("Hex string has odd length: " + quote(shorten(10, s)));
  int n = l(s) / 2;
  byte[] bytes = new byte[n];
  for (int i = 0; i < n; i++) {
    int a = parseHexChar(s.charAt(i*2));
    int b = parseHexChar(s.charAt(i*2+1));
    if (a < 0 || b < 0)
      throw fail("Bad hex byte: " + quote(substring(s, i*2, i*2+2)) + " at " + i*2 + "/" + l(s));
    bytes[i] = (byte) ((a << 4) | b);
  }
  return bytes;
}


public static <A> String join(String glue, Iterable<A> strings) {
  if (strings == null) return "";
  if (strings instanceof Collection) {
    if (((Collection) strings).size() == 1) return strOrEmpty(first((Collection) strings));
  }
  StringBuilder buf = new StringBuilder();
  Iterator<A> i = strings.iterator();
  if (i.hasNext()) {
    buf.append(strOrEmpty(i.next()));
    while (i.hasNext())
      buf.append(glue).append(strOrEmpty(i.next()));
  }
  return buf.toString();
}

public static String join(String glue, String... strings) {
  return join(glue, Arrays.asList(strings));
}

public static String join(String glue, Object... strings) {
  return join(glue, Arrays.asList(strings));
}

static <A> String join(Iterable<A> strings) {
  return join("", strings);
}

static <A> String join(Iterable<A> strings, String glue) {
  return join(glue, strings);
}

public static String join(String[] strings) {
  return join("", strings);
}


static String join(String glue, Pair p) {
  return p == null ? "" : str(p.a) + glue + str(p.b);
}



static String unnull(String s) {
  return s == null ? "" : s;
}

static <A> Collection<A> unnull(Collection<A> l) {
  return l == null ? emptyList() : l;
}

static <A> List<A> unnull(List<A> l) { return l == null ? emptyList() : l; }
static int[] unnull(int[] l) { return l == null ? emptyIntArray() : l; }
static char[] unnull(char[] l) { return l == null ? emptyCharArray() : l; }
static double[] unnull(double[] l) { return l == null ? emptyDoubleArray() : l; }
static float[] unnull(float[] l) { return l == null ? emptyFloatArray() : l; }

static <A, B> Map<A, B> unnull(Map<A, B> l) {
  return l == null ? emptyMap() : l;
}

static <A> Iterable<A> unnull(Iterable<A> i) {
  return i == null ? emptyList() : i;
}

static <A> A[] unnull(A[] a) {
  return a == null ? (A[]) emptyObjectArray() : a;
}

static BitSet unnull(BitSet b) {
  return b == null ? new BitSet() : b;
}


static Pt unnull(Pt p) {
  return p == null ? new Pt() : p;
}


//ifclass Symbol

static Symbol unnull(Symbol s) {
  return s == null ? emptySymbol() : s;
}
//endif



static <A, B> Pair<A, B> unnull(Pair<A, B> p) {
  return p != null ? p : new Pair(null, null);
}


static int unnull(Integer i) { return i == null ? 0 : i; }
static long unnull(Long l) { return l == null ? 0L : l; }
static double unnull(Double l) { return l == null ? 0.0 : l; }


// unclear semantics as to whether return null on null

static <A> ArrayList<A> asList(A[] a) {
  return a == null ? new ArrayList<A>() : new ArrayList<A>(Arrays.asList(a));
}

static ArrayList<Character> asList(char[] a) {
  if (a == null) return null;
  ArrayList<Character> l = emptyList(a.length);
  for (var i : a) l.add(i);
  return l;
}

static ArrayList<Byte> asList(byte[] a) {
  if (a == null) return null;
  ArrayList<Byte> l = emptyList(a.length);
  for (var i : a) l.add(i);
  return l;
}

static ArrayList<Integer> asList(int[] a) {
  if (a == null) return null;
  ArrayList<Integer> l = emptyList(a.length);
  for (int i : a) l.add(i);
  return l;
}

static ArrayList<Long> asList(long[] a) {
  if (a == null) return null;
  ArrayList<Long> l = emptyList(a.length);
  for (long i : a) l.add(i);
  return l;
}

static ArrayList<Float> asList(float[] a) {
  if (a == null) return null;
  ArrayList<Float> l = emptyList(a.length);
  for (float i : a) l.add(i);
  return l;
}

static ArrayList<Double> asList(double[] a) {
  if (a == null) return null;
  ArrayList<Double> l = emptyList(a.length);
  for (double i : a) l.add(i);
  return l;
}

static ArrayList<Short> asList(short[] a) {
  if (a == null) return null;
  ArrayList<Short> l = emptyList(a.length);
  for (short i : a) l.add(i);
  return l;
}

static <A> ArrayList<A> asList(Iterator<A> it) {
  ArrayList l = new ArrayList();
  if (it != null)
    while (it.hasNext())
      l.add(it.next());
  return l;  
}

// disambiguation
static <A> ArrayList<A> asList(IterableIterator<A> s) {
  return asList((Iterator) s);
}

static <A> ArrayList<A> asList(Iterable<A> s) {
  if (s instanceof ArrayList) return (ArrayList) s;
  ArrayList l = new ArrayList();
  if (s != null)
    for (A a : s)
      l.add(a);
  return l;
}



static <A> ArrayList<A> asList(Enumeration<A> e) {
  ArrayList l = new ArrayList();
  if (e != null)
    while (e.hasMoreElements())
      l.add(e.nextElement());
  return l;
}


static <A> ArrayList<A> asList(ReverseChain<A> c) {
  return c == null ? emptyList() : c.toList();
}



static <A> List<A> asList(Pair<A, A> p) {
  return p == null ? null : ll(p.a, p.b);
}





//static final Map<Class, HashMap<S, Field>> getOpt_cache = newDangerousWeakHashMap(f getOpt_special_init);

static class getOpt_Map extends WeakHashMap {
  getOpt_Map() {
    if (getOpt_special == null) getOpt_special = new HashMap();
    clear();
  }
  
  public void clear() {
    super.clear();
    //print("getOpt clear");
    put(Class.class, getOpt_special);
    put(String.class, getOpt_special);
  }
}

static final Map<Class, HashMap<String, Field>> getOpt_cache = 
  
  
    _registerDangerousWeakMap(synchroMap(new getOpt_Map()));
  
  
static HashMap getOpt_special; // just a marker

/*static void getOpt_special_init(Map map) {
  map.put(Class.class, getOpt_special);
  map.put(S.class, getOpt_special);
}*/

static Map<String, Field> getOpt_getFieldMap(Object o) {
  Class c = _getClass(o);
  HashMap<String, Field> map = getOpt_cache.get(c);
  if (map == null)
    map = getOpt_makeCache(c);
  return map;
}

static Object getOpt_cached(Object o, String field) { try {
  if (o == null) return null;

  Map<String, Field> map = getOpt_getFieldMap(o);

  if (map == getOpt_special) {
    if (o instanceof Class)
      return getOpt((Class) o, field);
    /*if (o instanceof S)
      ret getOpt(getBot((S) o), field);*/
    if (o instanceof Map)
      return ((Map) o).get(field);
  }
    
  Field f = map.get(field);
  if (f != null) return f.get(o);
  
    if (o instanceof DynamicObject)
      return syncMapGet2(((DynamicObject) o).fieldValues, field);
  
  return null;
} catch (Exception __e) { throw rethrow(__e); } }

// used internally - we are in synchronized block
static HashMap<String, Field> getOpt_makeCache(Class c) {
  HashMap<String, Field> map;
  if (isSubtypeOf(c, Map.class))
    map = getOpt_special;
  else {
    map = new HashMap();
    if (!reflection_classesNotToScan().contains(c.getName())) {
      Class _c = c;
      do {
        for (Field f : _c.getDeclaredFields()) {
          makeAccessible(f);
          String name = f.getName();
          if (!map.containsKey(name))
            map.put(name, f);
        }
        _c = _c.getSuperclass();
      } while (_c != null);
    }
  }
  if (getOpt_cache != null) getOpt_cache.put(c, map);
  return map;
}


static ThreadLocal<Object> print_byThread() {
  synchronized(print_byThread_lock) {
    if (print_byThread == null)
      print_byThread = new ThreadLocal();
  }
  return print_byThread;
}


// f can return false to suppress regular printing
// call print_raw within f to actually print something
static AutoCloseable tempInterceptPrint(F1<String, Boolean> f) {
  return tempSetThreadLocal(print_byThread(), f);
}


static boolean endsWithLetterOrDigit(String s) {
  return s != null && s.length() > 0 && Character.isLetterOrDigit(s.charAt(s.length()-1));
}


// PersistableThrowable doesn't hold GC-disturbing class references in backtrace
static volatile PersistableThrowable lastException_lastException;

static PersistableThrowable lastException() {
  return lastException_lastException;
}

static void lastException(Throwable e) {
  lastException_lastException = persistableThrowable(e);
}


static String hideCredentials(URL url) { return url == null ? null : hideCredentials(str(url)); }

static String hideCredentials(String url) {
  try {
    if (startsWithOneOf(url, "http://", "https://") && isAGIBlueDomain(hostNameFromURL(url))) return url;
  } catch (Throwable e) {
    print("HideCredentials", e);
  }
  return url.replaceAll("([&?])(_pass|key|cookie)=[^&\\s\"]*", "$1$2=<hidden>");
}

static String hideCredentials(Object o) {
  return hideCredentials(str(o));
}


static <A> int indexOf(List<A> l, A a, int startIndex) {
  if (l == null) return -1;
  int n = l(l);
  for (int i = startIndex; i < n; i++)
    if (eq(l.get(i), a))
      return i;
  return -1;
}

static <A> int indexOf(List<A> l, int startIndex, A a) {
  return indexOf(l, a, startIndex);
}

static <A> int indexOf(List<A> l, A a) {
  if (l == null) return -1;
  return l.indexOf(a);
}

static int indexOf(String a, String b) {
  return a == null || b == null ? -1 : a.indexOf(b);
}

static int indexOf(String a, String b, int i) {
  return a == null || b == null ? -1 : a.indexOf(b, i);
}

static int indexOf(String a, char b) {
  return a == null ? -1 : a.indexOf(b);
}

static int indexOf(String a, int i, char b) {
  return indexOf(a, b, i);
}

static int indexOf(String a, char b, int i) {
  return a == null ? -1 : a.indexOf(b, i);
}

static int indexOf(String a, int i, String b) {
  return a == null || b == null ? -1 : a.indexOf(b, i);
}

static <A> int indexOf(A[] x, A a) {
  int n = l(x);
  for (int i = 0; i < n; i++)
    if (eq(x[i], a))
      return i;
  return -1;
}

static <A> int indexOf(Iterable<A> l, A a) {
  if (l == null) return -1;
  int i = 0;
  for (A x : l) {
    if (eq(x, a))
      return i;
    i++;
  }
  return -1;
}



static void rotateStringBuffer(StringBuffer buf, int max) { try {
  if (buf == null) return;
  synchronized(buf) {
    if (buf.length() <= max) return;
    
    try {
      int newLength = max/2;
      int ofs = buf.length()-newLength;
      String newString = buf.substring(ofs);
      buf.setLength(0);
      buf.append("[...] ").append(newString);
    } catch (Exception e) {
      buf.setLength(0);
    }
    buf.trimToSize();
  }
} catch (Exception __e) { throw rethrow(__e); } }


static void rotateStringBuilder(StringBuilder buf, int max) { try {
  if (buf == null) return;
  synchronized(buf) {
    if (buf.length() <= max) return;
    
    try {
      int newLength = max/2;
      int ofs = buf.length()-newLength;
      String newString = buf.substring(ofs);
      buf.setLength(0);
      buf.append("[...] ").append(newString);
    } catch (Exception e) {
      buf.setLength(0);
    }
    buf.trimToSize();
  }
} catch (Exception __e) { throw rethrow(__e); } }


static int toInt(Object o) {
  if (o == null) return 0;
  if (o instanceof Number)
    return ((Number) o).intValue();
  if (o instanceof String)
    return parseInt((String) o);
  if (o instanceof Boolean)
    return boolToInt((Boolean) o);
  throw fail("woot not int: " + getClassName(o));
}

static int toInt(long l) {
  if (l != (int) l) throw fail("Too large for int: " + l);
  return (int) l;
}


static <A, B> Pair<A, B> mapEntryToPair(Map.Entry<A, B> e) {
  return e == null ? null : pair(e.getKey(), e.getValue());
}


static <A, B> Set<Map.Entry<A,B>> entrySet(Map<A, B> map) {
  return _entrySet(map);
}


static <A, B> Pair<A, B> pair(A a, B b) {
  return new Pair(a, b);
}

static <A> Pair<A, A> pair(A a) {
  return new Pair(a, a);
}


static <A> A firstThat(Iterable<A> l, IF1<A, Boolean> pred) {
  for (A a : unnullForIteration(l))
    if (pred.get(a))
      return a;
  return null;
}

static <A> A firstThat(A[] l, IF1<A, Boolean> pred) {
  for (A a : unnullForIteration(l))
    if (pred.get(a))
      return a;
  return null;
}

static <A> A firstThat(IF1<A, Boolean> pred, Iterable<A> l) {
  return firstThat(l, pred);
}

static <A> A firstThat(IF1<A, Boolean> pred, A[] l) {
  return firstThat(l, pred);
}



static <A> ArrayList<A> cloneList(Iterable<A> l) {
  return l instanceof Collection ? cloneList((Collection) l) : asList(l);
}

static <A> ArrayList<A> cloneList(Collection<A> l) {
  if (l == null) return new ArrayList();
  synchronized(collectionMutex(l)) {
    return new ArrayList<A>(l);
  }
}


static Object pcallF_minimalExceptionHandling(Object f, Object... args) {
  try {
    return callFunction(f, args);
  } catch (Throwable e) {
    System.out.println(getStackTrace(e));
    _storeException(e);
  }
  return null;
}


static Set vm_generalIdentityHashSet(Object name) {
  synchronized(vm_generalMap()) {
    Set set =  (Set) (vm_generalMap_get(name));
    if (set == null)
      vm_generalMap_put(name, set = syncIdentityHashSet());
    return set;
  }
}



static Map vm_generalHashMap(Object name) {
  synchronized(vm_generalMap()) {
    Map m =  (Map) (vm_generalMap_get(name));
    if (m == null)
      vm_generalMap_put(name, m = syncHashMap());
    return m;
  }
}



static TreeSet<String> litciset(String... items) {
  TreeSet<String> set = caseInsensitiveSet();
  for (String a : items) set.add(a);
  return set;
}


static TreeSet<Symbol> litciset(Symbol... items) {
  TreeSet<Symbol> set = treeSet(); // HashSet would also do, but we might have the return type fixed somewhere, and they might want a NavigableMap.
  for (Symbol a : items) set.add(a);
  return set;
}



static boolean contains(Collection c, Object o) {
  return c != null && c.contains(o);
}

static boolean contains(Iterable it, Object a) {
  if (it != null)
    for (Object o : it)
      if (eq(a, o))
        return true;
  return false;
}

static boolean contains(Object[] x, Object o) {
  if (x != null)
    for (Object a : x)
      if (eq(a, o))
        return true;
  return false;
}

static boolean contains(String s, char c) {
  return s != null && s.indexOf(c) >= 0;
}

static boolean contains(String s, String b) {
  return s != null && s.indexOf(b) >= 0;
}

static boolean contains(BitSet bs, int i) {
  return bs != null && bs.get(i);
}




static boolean contains(Rect r, Pt p) { return rectContains(r, p); }



static boolean ewic(String a, String b) {
  return endsWithIgnoreCase(a, b);
}


static boolean ewic(String a, String b, Matches m) {
  return endsWithIgnoreCase(a, b, m);
}



static String dropSuffixIgnoreCase(String suffix, String s) {
  return ewic(s, suffix) ? s.substring(0, l(s)-l(suffix)) : s;
}


static boolean ewicOneOf(String s, String... l) {
  if (s != null) for (String x : l) if (ewic(s, x)) return true; return false;
}


static Class javax() {
  return getJavaX();
}


static <A extends Throwable> A printException(A e) {
  printStackTrace(e);
  return e;
}


static <A> A assertNotNull(A a) {
  assertTrue(a != null);
  return a;
}

static <A> A assertNotNull(String msg, A a) {
  assertTrue(msg, a != null);
  return a;
}


static <A> A assertNotNull(Scorer scorer, String msg, A a) {
  if (scorer == null) return assertNotNull(msg, a);
  if (a == null) {
    print("BAD - " + msg + " is null: " + a);
    scorer.add(false);
  } else {
    print("OK, " + msg + " not null: " + a);
    scorer.add(true);
  }
  return a;
}



static Map synchroHashMap() {
  return synchronizedMap(new HashMap());
}



static <A> A vm_generalMap_getOrCreate(Object key, F0<A> create) {
  return vm_generalMap_getOrCreate(key, f0ToIF0(create));
}

static <A> A vm_generalMap_getOrCreate(Object key, IF0<A> create) {
  Map generalMap = vm_generalMap();
  if (generalMap == null) return null; // must be x30 init
  
  synchronized(generalMap) { // should switch to locks here
    A a =  (A) (vm_generalMap_get(key));
    if (a == null)
      vm_generalMap_put(key, a = create == null ? null : create.get());
    return a;
  }
}




  static <A> A callF_gen(F0<A> f) {
    return f == null ? null : f.get();
  }



  static <A, B> B callF_gen(F1<A, B> f, A a) {
    return f == null ? null : f.get(a);
  }



  static <A> A callF_gen(IF0<A> f) {
    return f == null ? null : f.get();
  }



  static <A, B> B callF_gen(IF1<A, B> f, A a) {
    return f == null ? null : f.get(a);
  }


static <A, B> B callF_gen(A a, IF1<A, B> f) {
  return f == null ? null : f.get(a);
}




  static <A, B, C> C callF_gen(IF2<A, B, C> f, A a, B b) {
    return f == null ? null : f.get(a, b);
  }



  static <A> void callF_gen(VF1<A> f, A a) {
    { if (f != null) f.get(a); }
  }


static <A> void callF_gen(A a, IVF1<A> f) {
  { if (f != null) f.get(a); }
}

static <A> void callF_gen(IVF1<A> f, A a) {
  { if (f != null) f.get(a); }
}

static Object callF_gen(Runnable r) { { if (r != null) r.run(); } return null; }

static Object callF_gen(Object f, Object... args) {
  return callF(f, args);
}


static Object vm_generalMap_get(Object key) {
  return vm_generalMap().get(key);
}


static final Map<Class, _MethodCache> callOpt_cache = newDangerousWeakHashMap();

static Object callOpt_cached(Object o, String methodName, Object... args) { try {
  if (o == null) return null;
  
  if (o instanceof Class) {
    Class c = (Class) o;
    _MethodCache cache = callOpt_getCache(c);
    
    // TODO: (super-rare) case where method exists static and non-static
    // with different args
    
    Method me = cache.findMethod(methodName, args);
    if (me == null || (me.getModifiers() & Modifier.STATIC) == 0) return null;
    return invokeMethod(me, null, args);
  } else {
    Class c = o.getClass();
    _MethodCache cache = callOpt_getCache(c);

    Method me = cache.findMethod(methodName, args);
    if (me == null) return null;
    return invokeMethod(me, o, args);
  }
} catch (Exception __e) { throw rethrow(__e); } }

// no longer synchronizes! (see #1102990)
static _MethodCache callOpt_getCache(Class c) {
  _MethodCache cache = callOpt_cache.get(c);
  if (cache == null)
    callOpt_cache.put(c, cache = new _MethodCache(c));
  return cache;
}


static boolean isStaticMethod(Method m) {
  return methodIsStatic(m);
}


static Object[] massageArgsForVarArgsCall(Executable m, Object[] args) {
  Class<?>[] types = m.getParameterTypes();
  int n = types.length-1, nArgs = l(args);
  if (nArgs < n) return null;
  for (int i = 0; i < n; i++)
    if (!argumentCompatibleWithType(args[i], types[i]))
      return null;
  Class varArgType = types[n].getComponentType();
  for (int i = n; i < nArgs; i++)
    if (!argumentCompatibleWithType(args[i], varArgType))
      return null;
  Object[] newArgs = new Object[n+1];
  arraycopy(args, 0, newArgs, 0, n);
  
  // TODO: optimize
  
  int nVarArgs = nArgs-n;
  Object varArgs = Array.newInstance(varArgType, nVarArgs);
  for (int i = 0; i < nVarArgs; i++)
    Array.set(varArgs, i, args[n+i]);
    
  newArgs[n] = varArgs;
  return newArgs;
}


static String formatArgumentClasses(Object[] args) {
  return joinWithComma(map(__23 -> getClassName(__23), args));
}


// TODO: optimize (use getOpt_cache)
static void setOpt_raw(Object o, String field, Object value) { try {
  if (o == null) return;
  if (o instanceof Class) setOpt_raw((Class) o, field, value);
  else {
    Field f = setOpt_raw_findField(o.getClass(), field);
    if (f != null) {
      makeAccessible(f);
      smartSet(f, o, value);
    }
  }
} catch (Exception __e) { throw rethrow(__e); } }

static void setOpt_raw(Class c, String field, Object value) { try {
  if (c == null) return;
  Field f = setOpt_raw_findStaticField(c, field);
  if (f != null) {
    makeAccessible(f);
    smartSet(f, null, value);
  }
} catch (Exception __e) { throw rethrow(__e); } }
  
static Field setOpt_raw_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}

static Field setOpt_raw_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}


static void smartSet(Field f, Object o, Object value) throws Exception {
  try {
    f.set(o, value);
  } catch (Exception e) {
    Class type = f.getType();
    
    // take care of common case (long to int)
    if (type == int.class && value instanceof Long)
      { f.set(o, ((Long) value).intValue()); return; }
      
    if (type == boolean.class && value instanceof String)
      { f.set(o, isTrueOrYes(((String) value))); return; }
    
    if (type == LinkedHashMap.class && value instanceof Map)
      { f.set(o, asLinkedHashMap((Map) value)); return; }
    
    
    throw e;
  }
}


static <A extends DynamicObject> A setDyn(A o, String key, Object value) {
  setDynObjectValue(o, key, value);
  return o;
}

static void setDyn(IMeta o, String key, Object value) {
  metaMapPut(o, key, value);
}


static Object pcallF(Object f, Object... args) {
  return pcallFunction(f, args);
}


static <A> A pcallF(F0<A> f) {
  try { return f == null ? null : f.get(); } catch (Throwable __e) { pcallFail(__e); } return null;
}



static <A, B> B pcallF(F1<A, B> f, A a) {
  try { return f == null ? null : f.get(a); } catch (Throwable __e) { pcallFail(__e); } return null;
}



static <A> void pcallF(VF1<A> f, A a) {
  try {
    { if (f != null) f.get(a); }
  } catch (Throwable __e) { pcallFail(__e); }
}


static Object pcallF(Runnable r) {
  try { { if (r != null) r.run(); } } catch (Throwable __e) { pcallFail(__e); } return null;
}

static <A> A pcallF(IF0<A> f) {
  try { return f == null ? null : f.get(); } catch (Throwable __e) { pcallFail(__e); } return null;
}

static <A, B> B pcallF(IF1<A, B> f, A a) {
  try { return f == null ? null : f.get(a); } catch (Throwable __e) { pcallFail(__e); } return null;
}



static String[] drop(int n, String[] a) {
  n = Math.min(n, a.length);
  String[] b = new String[a.length-n];
  System.arraycopy(a, n, b, 0, b.length);
  return b;
}

static Object[] drop(int n, Object[] a) {
  n = Math.min(n, a.length);
  Object[] b = new Object[a.length-n];
  System.arraycopy(a, n, b, 0, b.length);
  return b;
}

static <A> List<A> drop(Iterable<A> c, Object pred) {
  return antiFilter(c, pred);
}



static List drop(Object pred, Iterable c) {
  return antiFilter(pred, c);
}



static List drop(Object pred, Object[] c) {
  return antiFilter(pred, c);
}



static <A, B extends A> List<B> drop(Iterable<B> c, F1<A, Boolean> pred) {
  return antiFilter(c, pred);
}



static <A, B extends A> List<B> drop(F1<A, Boolean> pred, Iterable<B> c) {
  return antiFilter(pred, c);
}



static <A, B extends A> List<B> drop(Iterable<B> c, IF1<A, Boolean> pred) {
  return antiFilter(c, pred);
}



static <A, B extends A> List<B> drop(IF1<A, Boolean> pred, Iterable<B> c) {
  return antiFilter(pred, c);
}


static <A> ArrayList<A> toList(A[] a) { return asList(a); }
static ArrayList<Integer> toList(int[] a) { return asList(a); }
static ArrayList<Short> toList(short[] a) { return asList(a); }
static ArrayList<Long> toList(long[] a) { return asList(a); }
static <A> ArrayList<A> toList(Set<A> s) { return asList(s); }
static <A> ArrayList<A> toList(Iterable<A> s) { return asList(s); }


static String substring(String s, int x) {
  return substring(s, x, strL(s));
}

static String substring(String s, int x, int y) {
  if (s == null) return null;
  if (x < 0) x = 0;
  int n = s.length();
  if (y < x) y = x;
  if (y > n) y = n;
  if (x >= y) return "";
  return s.substring(x, y);
}



// convenience method for quickly dropping a prefix
static String substring(String s, CharSequence l) {
  return substring(s, lCharSequence(l));
}


static boolean isDigit(char c) {
  return Character.isDigit(c);
}


static int lastIndexOf(String a, String b) {
  return a == null || b == null ? -1 : a.lastIndexOf(b);
}

static int lastIndexOf(String a, char b) {
  return a == null ? -1 : a.lastIndexOf(b);
}

// starts searching from i-1
static <A> int lastIndexOf(List<A> l, int i, A a) {
  if (l == null) return -1;
  for (i = min(l(l), i)-1; i >= 0; i--)
    if (eq(l.get(i), a))
      return i;
  return -1;
}

static <A> int lastIndexOf(List<A> l, A a) {
  if (l == null) return -1;
  for (int i = l(l)-1; i >= 0; i--)
    if (eq(l.get(i), a))
      return i;
  return -1;
}


static HashMap<String, List<Method>> callMC_cache = new HashMap();
static String callMC_key;
static Method callMC_value;

// varargs assignment fixer for a single string array argument
static Object callMC(String method, String[] arg) {
  return callMC(method, new Object[] {arg});
}

static Object callMC(String method, Object... args) { try {
  Method me;
  if (callMC_cache == null) callMC_cache = new HashMap(); // initializer time workaround
  synchronized(callMC_cache) {
    me = method == callMC_key ? callMC_value : null;
  }
  if (me != null) try {
    return invokeMethod(me, null, args);
  } catch (IllegalArgumentException e) {
    throw new RuntimeException("Can't call " + me + " with arguments " + classNames(args), e);
  }

  List<Method> m;
  synchronized(callMC_cache) {
    m = callMC_cache.get(method);
  }
  if (m == null) {
    if (callMC_cache.isEmpty()) {
      callMC_makeCache();
      m = callMC_cache.get(method);
    }
    if (m == null) throw fail("Method named " + method + " not found in main");
  }
  int n = m.size();
  if (n == 1) {
    me = m.get(0);
    synchronized(callMC_cache) {
      callMC_key = method;
      callMC_value = me;
    }
    try {
      return invokeMethod(me, null, args);
    } catch (IllegalArgumentException e) {
      throw new RuntimeException("Can't call " + me + " with arguments " + classNames(args), e);
    }
  }
  for (int i = 0; i < n; i++) {
    me = m.get(i);
    if (call_checkArgs(me, args, false))
      return invokeMethod(me, null, args);
  }
  throw fail("No method called " + method + " with arguments (" + joinWithComma(getClasses(args)) + ") found in main");
} catch (Exception __e) { throw rethrow(__e); } }

static void callMC_makeCache() {
  synchronized(callMC_cache) {
    callMC_cache.clear();
    Class _c = (Class) mc(), c = _c;
    while (c != null) {
      for (Method m : c.getDeclaredMethods())
        if ((m.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0) {
          makeAccessible(m);
          multiMapPut(callMC_cache, m.getName(), m);
        }
      c = c.getSuperclass();
    }
  }
}


static List<String> getClassNames(Collection l) {
  List<String> out = new ArrayList();
  if (l != null) for (Object o : l)
    out.add(o == null ? null : getClassName(o));
  return out;
}


static int shorten_default = 100;

static String shorten(CharSequence s) { return shorten(s, shorten_default); }

static String shorten(CharSequence s, int max) {
  return shorten(s, max, "...");
}

static String shorten(CharSequence s, int max, String shortener) {
  if (s == null) return "";
  if (max < 0) return str(s);
  return s.length() <= max ? str(s) : subCharSequence(s, 0, min(s.length(), max-l(shortener))) + shortener;
}

static String shorten(int max, CharSequence s) { return shorten(s, max); }


static int parseHexChar(char c) {
  if (c >= '0' && c <= '9') return charDiff(c, '0');
  if (c >= 'a' && c <= 'f') return charDiff(c, 'a')+10;
  if (c >= 'A' && c <= 'F') return charDiff(c, 'A')+10;
  return -1;
}


static String strOrEmpty(Object o) {
  return o == null ? "" : str(o);
}


static ArrayList emptyList() {
  return new ArrayList();
  //ret Collections.emptyList();
}

static ArrayList emptyList(int capacity) {
  return new ArrayList(max(0, capacity));
}

// Try to match capacity
static ArrayList emptyList(Iterable l) {
  return l instanceof Collection ? emptyList(((Collection) l).size()) : emptyList();
}

static ArrayList emptyList(Object[] l) {
  return emptyList(l(l));
}

// get correct type at once
static <A> ArrayList<A> emptyList(Class<A> c) {
  return new ArrayList();
}


static int[] emptyIntArray_a = new int[0];
static int[] emptyIntArray() { return emptyIntArray_a; }


static char[] emptyCharArray = new char[0];
static char[] emptyCharArray() { return emptyCharArray; }


static double[] emptyDoubleArray = new double[0];
static double[] emptyDoubleArray() { return emptyDoubleArray; }


static float[] emptyFloatArray = new float[0];
static float[] emptyFloatArray() { return emptyFloatArray; }


static Map emptyMap() {
  return new HashMap();
}


static Object[] emptyObjectArray_a = new Object[0];
static Object[] emptyObjectArray() { return emptyObjectArray_a; }


static Symbol emptySymbol_value;

static Symbol emptySymbol() {
  if (emptySymbol_value == null) emptySymbol_value = symbol("");
  return emptySymbol_value;
}




static void clear(Collection c) {
  if (c != null) c.clear();
}

static void clear(Map map) {
  if (map != null) map.clear();
}


static <A, B> void put(Map<A, B> map, A a, B b) {
  if (map != null) map.put(a, b);
}

static <A> void put(List<A> l, int i, A a) {
  if (l != null && i >= 0 && i < l(l)) l.set(i, a);
}


static Class<?> _getClass(String name) {
  try {
    return Class.forName(name);
  } catch (ClassNotFoundException e) {
    return null; // could optimize this
  }
}

static Class _getClass(Object o) {
  return o == null ? null
    : o instanceof Class ? (Class) o : o.getClass();
}

static Class _getClass(Object realm, String name) {
  try {
    return classLoaderForObject(realm).loadClass(classNameToVM(name));
  } catch (ClassNotFoundException e) {
    return null; // could optimize this
  }
}


static <A, B> B syncMapGet2(Map<A, B> map, A a) {
  if (map == null) return null;
  synchronized(collectionMutex(map)) {
    return map.get(a);
  }
}

static <A, B> B syncMapGet2(A a, Map<A, B> map) {
  return syncMapGet2(map, a);
}


static boolean isSubtypeOf(Class a, Class b) {
  return a != null && b != null && b.isAssignableFrom(a); // << always hated that method, let's replace it!
}


static Set<String> reflection_classesNotToScan_value = litset(
  "jdk.internal.loader.URLClassPath"
);

static Set<String> reflection_classesNotToScan() {
  return reflection_classesNotToScan_value;
}


static <A> AutoCloseable tempSetThreadLocal(final ThreadLocal<A> tl, A a) {
  if (tl == null) return null;
  final A prev = setThreadLocal(tl, a);
  return new AutoCloseable() { public String toString() { return "tl.set(prev);"; } public void close() throws Exception { tl.set(prev); }};
}


static PersistableThrowable persistableThrowable(Throwable e) {
  return e == null ? null : new PersistableThrowable(e);
}


static boolean startsWithOneOf(String s, String... l) {
  for (String x : l) if (startsWith(s, x)) return true; return false;
}

static boolean startsWithOneOf(String s, Matches m, String... l) {
  for (String x : l) if (startsWith(s, x, m)) return true; return false;
}


static boolean isAGIBlueDomain(String domain) {
  return domainIsUnder(domain, theAGIBlueDomain());
}


static String hostNameFromURL(String url) { try {
  return empty(url) ? null : new URL(url).getHost();
} catch (Exception __e) { throw rethrow(__e); } }


static int parseInt(String s) {
  return emptyString(s) ? 0 : Integer.parseInt(s);
}

static int parseInt(char c) {
  return Integer.parseInt(str(c));
}


static int boolToInt(boolean b) {
  return b ? 1 : 0;
}


static <A, B> Set<Map.Entry<A,B>> _entrySet(Map<A, B> map) {
  return map == null ? Collections.EMPTY_SET : map.entrySet();
}


static String unnullForIteration(String s) {
  return s == null ? "" : s;
}

static <A> Collection<A> unnullForIteration(Collection<A> l) {
  return l == null ? immutableEmptyList() : l;
}

static <A> List<A> unnullForIteration(List<A> l) { return l == null ? immutableEmptyList() : l; }
static byte[] unnullForIteration(byte[] l) { return l == null ? emptyByteArray() : l; }
static int[] unnullForIteration(int[] l) { return l == null ? emptyIntArray() : l; }
static char[] unnullForIteration(char[] l) { return l == null ? emptyCharArray() : l; }
static double[] unnullForIteration(double[] l) { return l == null ? emptyDoubleArray() : l; }
static short[] unnullForIteration(short[] l) { return l == null ? emptyShortArray() : l; }

static <A, B> Map<A, B> unnullForIteration(Map<A, B> l) {
  return l == null ? immutableEmptyMap() : l;
}

static <A> Iterable<A> unnullForIteration(Iterable<A> i) {
  return i == null ? immutableEmptyList() : i;
}

static <A> A[] unnullForIteration(A[] a) {
  return a == null ? (A[]) emptyObjectArray() : a;
}

static BitSet unnullForIteration(BitSet b) {
  return b == null ? new BitSet() : b;
}


static Pt unnullForIteration(Pt p) {
  return p == null ? new Pt() : p;
}


//ifclass Symbol

static Symbol unnullForIteration(Symbol s) {
  return s == null ? emptySymbol() : s;
}
//endif



static <A, B> Pair<A, B> unnullForIteration(Pair<A, B> p) {
  return p != null ? p : new Pair(null, null);
}


static long unnullForIteration(Long l) { return l == null ? 0L : l; }


// TODO: JDK 17!! ?? No! Yes? Yes!!

static Object collectionMutex(List l) {
  return l;
}

static Object collectionMutex(Object o) {
  

  if (o instanceof List) return o;
  
  // TODO: actually use our own maps so we can get the mutex properly
  
  String c = className(o);
  
    
  
    
  
  return o;
}


static Object callFunction(Object f, Object... args) {
  return callF(f, args);
}


static Throwable _storeException_value;

static void _storeException(Throwable e) {
  _storeException_value = e;
}


static Map vm_generalMap_map;

static Map vm_generalMap() {
  if (vm_generalMap_map == null)
    
    
    
    vm_generalMap_map = (Map) get(javax(), "generalMap");
    
    
  return vm_generalMap_map;
}


static Object vm_generalMap_put(Object key, Object value) {
  return mapPutOrRemove(vm_generalMap(), key, value);
}


static <A> Set<A> syncIdentityHashSet() {
  return (Set) synchronizedSet(identityHashSet());
}


static Map syncHashMap() {
  return synchroHashMap();
}


static TreeSet<String> caseInsensitiveSet() {
  return caseInsensitiveSet_treeSet();
}

static TreeSet<String> caseInsensitiveSet(Collection<String> c) {
  return caseInsensitiveSet_treeSet(c);
}


static <A> TreeSet<A> treeSet() {
  return new TreeSet();
}


static boolean rectContains(int x1, int y1, int w, int h, Pt p) {
  return p.x >= x1 && p.y >= y1 && p.x < x1+w && p.y < y1+h;
}

static boolean rectContains(Rect a, Rect b) {
  return b.x >= a.x && b.y >= a.y && b.x2() <= a.x2() && b.y2() <= a.y2();
}

static boolean rectContains(Rect a, Rectangle b) {
  return rectContains(a, toRect(b));
}

static boolean rectContains(Rect a, int x, int y) {
  return a != null && a.contains(x, y);
}

static boolean rectContains(Rect a, Pt p) {
  return a != null && p != null && a.contains(p);
}


static boolean endsWithIgnoreCase(String a, String b) {
  int la = l(a), lb = l(b);
  return la >= lb && regionMatchesIC(a, la-lb, b, 0, lb);
}


static boolean endsWithIgnoreCase(String a, String b, Matches m) {
  if (!endsWithIgnoreCase(a, b)) return false;
  if (m != null)
    m.m = new String[] { substring(a, 0, l(a)-l(b)) };
  return true;
}



static <A extends Throwable> A printStackTrace(A e) {
  // we go to system.out now - system.err is nonsense
  if (e != null) print(getStackTrace(e));
  return e;
}

static void printStackTrace() {
  printStackTrace(new Throwable());
}

static void printStackTrace(String msg) {
  printStackTrace(new Throwable(msg));
}

static void printStackTrace(String msg, Throwable e) {
  printStackTrace(new Throwable(msg, e));
}


static Map synchronizedMap() {
  return synchroMap();
}

static <A, B> Map<A, B> synchronizedMap(Map<A, B> map) {
  return synchroMap(map);
}


static <A> IF0<A> f0ToIF0(F0<A> f) {
  return f == null ? null : () -> f.get();
}


static boolean methodIsStatic(Method m) {
  return (m.getModifiers() & Modifier.STATIC) != 0;
}


static boolean argumentCompatibleWithType(Object arg, Class type) {
  return arg == null ? !type.isPrimitive() : isInstanceX(type, arg);
}


static void arraycopy(Object[] a, Object[] b) {
  if (a != null && b != null)
    arraycopy(a, 0, b, 0, Math.min(a.length, b.length));
}

static void arraycopy(Object src, int srcPos, int destPos, int n) { arraycopy(src, srcPos, src, destPos, n); }
static void arraycopy(Object src, int srcPos, Object dest, int destPos, int n) {
  if (n != 0)
    System.arraycopy(src, srcPos, dest, destPos, n);
}



static List map(Iterable l, Object f) { return map(f, l); }

static List map(Object f, Iterable l) {
  List x = emptyList(l);
  if (l != null) for  (Object o : l)
    { ping(); x.add(callF(f, o)); }
  return x;
}

// map: func(key, value) -> list element
static List map(Map map, Object f) {
  List x = new ArrayList();
  if (map != null) for  (Object _e : map.entrySet()) { ping(); 
    Map.Entry e = (Map.Entry) _e;
    x.add(callF(f, e.getKey(), e.getValue()));
  }
  return x;
}

static List map(Object f, Object[] l) { return map(f, asList(l)); }
static List map(Object[] l, Object f) { return map(f, l); }

static List map(Object f, Map map) {
  return map(map, f);
}




  static <A, B> List<B> map(Iterable<A> l, F1<A, B> f) { return map(f, l); }

  static <A, B> List<B> map(F1<A, B> f, Iterable<A> l) {
    List x = emptyList(l);
    if (l != null) for  (A o : l)
      { ping(); x.add(callF(f, o)); }
    return x;
  }


static <A, B> List<B> map(IF1<A, B> f, Iterable<A> l) { return map(l, f); }
static <A, B> List<B> map(Iterable<A> l, IF1<A, B> f) {
  List x = emptyList(l);
  if (l != null) {
    var it = l.iterator();
    if (it.hasNext()) {
      var pingSource = pingSource();
      do {
        ping(pingSource);
        x.add(f.get(it.next()));
      } while (it.hasNext());
    }
  }
  return x;
}
  
static <A, B> List<B> map(IF1<A, B> f, A[] l) { return map(l, f); }
static <A, B> List<B> map(A[] l, IF1<A, B> f) {
  List x = emptyList(l);
  if (l != null) for  (A o : l)
    { ping(); x.add(f.get(o)); }
  return x;
}
  
static <A, B, C> List<C> map(Map<A, B> map, IF2<A, B, C> f) {
  List x = new ArrayList();
  if (map != null) for  (Map.Entry<A, B> e : map.entrySet()) { ping(); 
    x.add(f.get(e.getKey(), e.getValue()));
  }
  return x;
}

// new magic alias for mapLL - does it conflict?

static <A, B> List<A> map(IF1<A, B> f, A data1, A... moreData) {
  List x = emptyList(l(moreData)+1);
  x.add(f.get(data1));
  if (moreData != null) for  (A o : moreData)
    { ping(); x.add(f.get(o)); }
  return x;
}


static boolean isTrueOrYes(Object o) {
  return isTrueOpt(o) || o instanceof String && (eqicOneOf(((String) o), "1", "t", "true") || isYes(((String) o)));
}


static <A, B> LinkedHashMap<A, B> asLinkedHashMap(Map<A, B> map) {
  if (map instanceof LinkedHashMap) return (LinkedHashMap) map;
  LinkedHashMap<A, B> m = new LinkedHashMap();
  if (map != null) synchronized(collectionMutex(map)) {
    m.putAll(map);
  }
  return m;
}


static void setDynObjectValue(DynamicObject o, String field, Object value) {
  dynamicObject_setRawFieldValue(o, field, value);
}


static void metaMapPut(IMeta o, Object key, Object value) {
  { if (o != null) o.metaPut(key, value); }
}

static void metaMapPut(Object o, Object key, Object value) {
  var meta = initIMeta(o);
  { if (meta != null) meta.metaPut(key, value); }
}


static Object pcallFunction(Object f, Object... args) {
  try { return callFunction(f, args); } catch (Throwable __e) { pcallFail(__e); }
  return null;
}


static void pcallFail(Throwable e) {
  pcallPolicyForThread().handlePcallFail(e);
}

static void pcallFail(String msg) {
  pcallFail(new Throwable(msg));
}


static <A> List<A> antiFilter(Iterable<A> c, Object pred) {
  if (pred instanceof F1) return antiFilter(c, (F1<A, Boolean>) pred);

  List x = new ArrayList();
  if (c != null) for (Object o : c)
    if (!isTrue(callF(pred, o)))
      x.add(o);
  return x;
}

static List antiFilter(Object pred, Iterable c) {
  return antiFilter(c, pred);
}

static List antiFilter(Object pred, Object[] c) {
  return antiFilter(pred, wrapArrayAsList(c));
}

static <A, B extends A> List<B> antiFilter(Iterable<B> c, F1<A, Boolean> pred) {
  List x = new ArrayList();
  if (c != null) for (B o : c)
    if (!pred.get(o).booleanValue())
      x.add(o);
  return x;
}

static <A, B extends A> List<B> antiFilter(F1<A, Boolean> pred, Iterable<B> c) {
  return antiFilter(c, pred);
}

static <A, B extends A> List<B> antiFilter(Iterable<B> c, IF1<A, Boolean> pred) {
  List x = new ArrayList();
  if (c != null) for (B o : c)
    if (!pred.get(o).booleanValue())
      x.add(o);
  return x;
}

static <A, B extends A> List<B> antiFilter(IF1<A, Boolean> pred, Iterable<B> c) {
  return antiFilter(c, pred);
}



static int strL(String s) {
  return s == null ? 0 : s.length();
}


static int lCharSequence(CharSequence s) {
  return s == null ? 0 : s.length();
}


static List<Class> getClasses(Object[] array) {
  List<Class> l = emptyList(l(array));
  for (Object o : array) l.add(_getClass(o));
  return l;
}


static <A, B> void multiMapPut(Map<A, List<B>> map, A a, B b) {
  List<B> l = map.get(a);
  if (l == null)
    map.put(a, l = new ArrayList());
  l.add(b);
}


static <A, B> void multiMapPut(MultiMap<A, B> mm, A key, B value) {
  if (mm != null && key != null && value != null) mm.put(key, value);
}



static CharSequence subCharSequence(CharSequence s, int x) {
  return subCharSequence(s, x, s == null ? 0 : s.length());
}

static CharSequence subCharSequence(CharSequence s, int x, int y) {
  if (s == null) return null;
  if (x < 0) x = 0;
  if (x >= s.length()) return "";
  if (y < x) y = x;
  if (y > s.length()) y = s.length();
  return s.subSequence(x, y);
}


static int charDiff(char a, char b) {
  return (int) a-(int) b;
}

static int charDiff(String a, char b) {
  return charDiff(stringToChar(a), b);
}




static WeakHasherMap<Symbol, Boolean> symbol_map = new WeakHasherMap(new Hasher<Symbol>() {
  public int hashCode(Symbol symbol) { return symbol.text.hashCode(); }
  public boolean equals(Symbol a, Symbol b) {
    if (a == null) return b == null;
    return b != null && eq(a.text, b.text);
  }
});



static Symbol symbol(String s) {
  
  
  if (s == null) return null;
  synchronized(symbol_map) {
    // TODO: avoid object creation by passing the string to findKey
    Symbol symbol = new Symbol(s, true);
    Symbol existingSymbol = symbol_map.findKey(symbol);
    if (existingSymbol == null)
      symbol_map.put(existingSymbol = symbol, true);
    
      
    return existingSymbol;
  }
  
}

static Symbol symbol(CharSequence s) {
  if (s == null) return null;
  
  
  if (s instanceof Symbol) return (Symbol) s;
  if (s instanceof String) return symbol((String) s);
  return symbol(str(s));
  
}

static Symbol symbol(Object o) {
  return symbol((CharSequence) o);
}




static ClassLoader classLoaderForObject(Object o) {
  if (o instanceof ClassLoader) return ((ClassLoader) o);
  if (o == null) return null;
  return _getClass(o).getClassLoader();
}


// Note: This is actually broken. Inner classes must stay with a $ separator
static String classNameToVM(String name) {
  return name.replace(".", "$");
}


static <A> HashSet<A> litset(A... items) {
  return lithashset(items);
}


static <A> A setThreadLocal(ThreadLocal<A> tl, A value) {
  if (tl == null) return null;
  A old = tl.get();
  tl.set(value);
  return old;
}


static boolean startsWith(String a, String b) {
  return a != null && a.startsWith(unnull(b));
}

static boolean startsWith(String a, char c) {
  return nemptyString(a) && a.charAt(0) == c;
}


  static boolean startsWith(String a, String b, Matches m) {
    if (!startsWith(a, b)) return false;
    if (m != null) m.m = new String[] {substring(a, strL(b))};
    return true;
  }


static boolean startsWith(List a, List b) {
  if (a == null || listL(b) > listL(a)) return false;
  for (int i = 0; i < listL(b); i++)
    if (neq(a.get(i), b.get(i)))
      return false;
  return true;
}




static boolean domainIsUnder(String domain, String mainDomain) {
  return eqic(domain, mainDomain) || ewic(domain, "." + mainDomain);
}


static String theAGIBlueDomain() {
  return "agi.blue";
}


static boolean emptyString(String s) {
  return s == null || s.length() == 0;
}


static <A> List<A> immutableEmptyList() {
  return Collections.emptyList();
}


static byte[] emptyByteArray_a = new byte[0];
static byte[] emptyByteArray() { return emptyByteArray_a; }


static short[] emptyShortArray = new short[0];
static short[] emptyShortArray() { return emptyShortArray; }


static <A, B> Map<A, B> immutableEmptyMap() {
  return Collections.emptyMap();
}


static <A, B> B mapPutOrRemove(Map<A, B> map, A key, B value) {
  if (map != null && key != null)
    if (value != null) return map.put(key, value);
    else return map.remove(key);
  return null;
}


static <A> Set<A> synchronizedSet() {
  return synchroHashSet();
}

static <A> Set<A> synchronizedSet(Set<A> set) {
  
  
    return Collections.synchronizedSet(set);
  
}


static <A> Set<A> identityHashSet() {
  return Collections.newSetFromMap(new IdentityHashMap());
}


static TreeSet<String> caseInsensitiveSet_treeSet() {
  return new TreeSet(caseInsensitiveComparator());
}

static TreeSet<String> caseInsensitiveSet_treeSet(Collection<String> c) {
  return toCaseInsensitiveSet_treeSet(c);
}




static Rect toRect(Rectangle r) {
  return r == null ? null : new Rect(r);
}

static Rect toRect(RectangularShape r) {
  return r == null ? null : toRect(r.getBounds());
}


static Rect toRect(DoubleRect r) {
  if (r == null) return null;
  int x = iround(r.x), y = iround(r.y);
  return new Rect(x, y, iround(r.x2())-x, iround(r.y2())-y);
}


static Rect toRect(Rect r) { return r; }


static boolean regionMatchesIC(String a, int offsetA, String b, int offsetB, int len) {
  
  
    return a != null && a.regionMatches(true, offsetA, b, offsetB, len);
  
}


// assumptions:
// -pingSource() stays constant within a stack frame (so you can cache it)
// -all changes happen with tempSetPingSource
// -multiple threads can share a PingSource
static PingSource pingSource() {
  return pingSource_tl().get();
}

static PingSource pingSource(Thread thread) {
  return pingSource_tl().get(thread);
}


static boolean isTrueOpt(Object o) {
  if (o instanceof Boolean)
    return ((Boolean) o).booleanValue();
  return false;
}

static boolean isTrueOpt(String field, Object o) {
  return isTrueOpt(getOpt(field, o));
}


static boolean eqicOneOf(String s, String... l) {
  for (String x : l) if (eqic(s, x)) return true; return false;
}


static List<String> isYes_yesses = litlist("y", "yes", "yeah", "y", "yup", "yo", "corect", "sure", "ok", "afirmative"); // << collapsed words, so "corect" means "correct"

static boolean isYes(String s) {
  return isYes_yesses.contains(collapseWord(toLowerCase(firstWord2(s))));
}


static void dynamicObject_setRawFieldValue(DynamicObject o, Object key, Object value) {
  if (o == null) return;
  
  // double sync, but should be OK here because of locking order o > o.fieldValues
  synchronized(o) {
    o.fieldValues = syncMapPut2_createLinkedHashMap((LinkedHashMap) o.fieldValues, key, value);
  }
}


static IMeta initIMeta(Object o) {
  if (o == null) return null;
  if (o instanceof IMeta) return ((IMeta) o);
  if (o instanceof JComponent) return initMetaOfJComponent((JComponent) o);
  
  // This is not really used. Try to use BufferedImageWithMeta instead
  if (o instanceof BufferedImage) return optCast(IMeta.class, ((BufferedImage) o).getProperty("meta"));
  return null;
}


static PCallPolicy pcallPolicyForThread() {
  var policy = pcallPolicyForThread_tl().get();
  if (policy != null) return policy;
  return defaultPCallPolicy();
}


static <A> List<A> wrapArrayAsList(A[] a) {
  return a == null ? null : Arrays.asList(a);
}


static char stringToChar(String s) {
  if (l(s) != 1) throw fail("bad stringToChar: " + s);
  return firstChar(s);
}




static <A> HashSet<A> lithashset(A... items) {
  HashSet<A> set = new HashSet();
  for (A a : items) set.add(a);
  return set;
}


static boolean nemptyString(String s) {
  return s != null && s.length() > 0;
}


static int listL(Collection l) {
  return l == null ? 0 : l.size();
}


static boolean neq(Object a, Object b) {
  return !eq(a, b);
}


static boolean eqic(String a, String b) {
  
  
    if ((a == null) != (b == null)) return false;
    if (a == null) return true;
    return a.equalsIgnoreCase(b);
  
}


static boolean eqic(Symbol a, Symbol b) {
  return eq(a, b);
}

static boolean eqic(Symbol a, String b) {
  return eqic(asString(a), b);
}


static boolean eqic(char a, char b) {
  if (a == b) return true;
  
    char u1 = Character.toUpperCase(a);
    char u2 = Character.toUpperCase(b);
    if (u1 == u2) return true;
  
  return Character.toLowerCase(u1) == Character.toLowerCase(u2);
}


static <A> Set<A> synchroHashSet() {
  return synchronizedSet(new HashSet<A>());
}



static Comparator<String> caseInsensitiveComparator() {
  
  
  return betterCIComparator();
  
}


static TreeSet<String> toCaseInsensitiveSet_treeSet(Iterable<String> c) {
  if (isCISet(c)) return (TreeSet) c;
  TreeSet<String> set = caseInsensitiveSet_treeSet();
  addAll(set, c);
  return set;
}

static TreeSet<String> toCaseInsensitiveSet_treeSet(String... x) {
  TreeSet<String> set = caseInsensitiveSet_treeSet();
  addAll(set, x);
  return set;
}


static int iround(double d) {
  return (int) Math.round(d);
}


static int iround(Number n) {
  return iround(toDouble(n));
}





static BetterThreadLocal<PingSource> pingSource_tl_var = new BetterThreadLocal<PingSource>() {
  @Override
  public PingSource initialValue() {
    return ping_v3_pingSourceMaker().get(); 
  }
};

static BetterThreadLocal<PingSource> pingSource_tl() {
  return pingSource_tl_var;
}


static <A> ArrayList<A> litlist(A... a) {
  ArrayList l = new ArrayList(a.length);
  for (A x : a) l.add(x);
  return l;
}


static String collapseWord(String s) {
  if (s == null) return "";
  StringBuilder buf = new StringBuilder();
  for (int i = 0; i < l(s); i++)
    if (i == 0 || !charactersEqualIC(s.charAt(i), s.charAt(i-1)))
      buf.append(s.charAt(i));
  return buf.toString();
}


static List<String> toLowerCase(List<String> strings) {
  List<String> x = new ArrayList();
  for (String s : strings)
    x.add(s.toLowerCase());
  return x;
}

static String[] toLowerCase(String[] strings) {
  String[] x = new String[l(strings)];
  for (int i = 0; i < l(strings); i++)
    x[i] = strings[i].toLowerCase();
  return x;
}

static String toLowerCase(String s) {
  return s == null ? "" : s.toLowerCase();
}


static String firstWord2(String s) {
  s = xltrim(s);
  if (empty(s)) return "";
  if (isLetterOrDigit(first(s)))
    return takeCharsWhile(__24 -> isLetterOrDigit(__24), s);
  else return "" + first(s);
}


static <A, B> LinkedHashMap<A, B> syncMapPut2_createLinkedHashMap(LinkedHashMap<A, B> map, A key, B value) {
  if (key != null)
    if (value != null) {
      if (map == null) map = new LinkedHashMap();
      synchronized(collectionMutex(map)) { map.put(key, value); }
    } else if (map != null) synchronized(collectionMutex(map)) { map.remove(key); }
  return map;
}


static IMeta initMetaOfJComponent(JComponent c) {
  if (c == null) return null;
  IMeta meta =  (IMeta) (c.getClientProperty(IMeta.class));
  if (meta == null)
    c.putClientProperty(IMeta.class, meta = new Meta());
  
  return meta;
}


static <A> A optCast(Class<A> c, Object o) {
  return isInstance(c, o) ? (A) o : null;
}




static ThreadLocal<PCallPolicy> pcallPolicyForThread_tl_tl = new ThreadLocal();

static ThreadLocal<PCallPolicy> pcallPolicyForThread_tl() {
  return pcallPolicyForThread_tl_tl;
}


static PCallPolicy defaultPCallPolicy = __1 -> printStackTrace(__1);

static PCallPolicy defaultPCallPolicy() {
  return defaultPCallPolicy;
}

static void defaultPCallPolicy_set(PCallPolicy policy) {
  defaultPCallPolicy = policy;
}


static char firstChar(String s) {
  return s.charAt(0);
}




static String asString(Object o) {
  return o == null ? null : o.toString();
}


static betterCIComparator_C betterCIComparator_instance;

static betterCIComparator_C betterCIComparator() {
  if (betterCIComparator_instance == null)
    betterCIComparator_instance = new betterCIComparator_C();
  return betterCIComparator_instance;
}

final static class betterCIComparator_C implements Comparator<String> {
  public int compare(String s1, String s2) {
    if (s1 == null) return s2 == null ? 0 : -1;
    if (s2 == null) return 1;
  
    int n1 = s1.length();
    int n2 = s2.length();
    int min = Math.min(n1, n2);
    for (int i = 0; i < min; i++) {
        char c1 = s1.charAt(i);
        char c2 = s2.charAt(i);
        if (c1 != c2) {
            c1 = Character.toUpperCase(c1);
            c2 = Character.toUpperCase(c2);
            if (c1 != c2) {
                c1 = Character.toLowerCase(c1);
                c2 = Character.toLowerCase(c2);
                if (c1 != c2) {
                    // No overflow because of numeric promotion
                    return c1 - c2;
                }
            }
        }
    }
    return n1 - n2;
  }
}


static boolean isCISet(Iterable<String> l) {
  return l instanceof TreeSet && ((TreeSet) l).comparator() == caseInsensitiveComparator();
}


static <A, B extends A> void addAll(Collection<A> c, Iterable<B> b) {
  if (c != null && b != null) for (A a : b) c.add(a);
}

static <A, B extends A> boolean addAll(Collection<A> c, Collection<B> b) {
  return c != null && b != null && c.addAll(b);
}

static <A, B extends A> boolean addAll(Collection<A> c, B... b) {
  return c != null && b != null && c.addAll(Arrays.asList(b));
}



static <A, B> Map<A, B> addAll(Map<A, B> a, Map<? extends A,? extends B> b) {
  if (a != null && b != null) a.putAll(b);
  return a;
}

static <A extends Container> A addAll(A c, Collection<? extends Component> components) {
  return addComponents(c, components);
}

static <A extends Container> A addAll(A c, Component... components) {
  return addComponents(c, components);
}


static double toDouble(Object o) {
  if (o instanceof Number)
    return ((Number) o).doubleValue();
  if (o instanceof BigInteger)
    return ((BigInteger) o).doubleValue();
  if (o instanceof String)
    return parseDouble((String) o);
  if (o == null) return 0.0;
  throw fail(o);
}


static IF0<PingSource> ping_v3_pingSourceMaker_cache;
static IF0<PingSource> ping_v3_pingSourceMaker() { if (ping_v3_pingSourceMaker_cache == null) ping_v3_pingSourceMaker_cache = ping_v3_pingSourceMaker_load(); return ping_v3_pingSourceMaker_cache;}

static IF0<PingSource> ping_v3_pingSourceMaker_load() {
  return or((IF0) vm_generalMap_get("ping_v3_pingSourceMaker"), () -> null);
}



static boolean charactersEqualIC(char c1, char c2) {
  if (c1 == c2) return true;
  char u1 = Character.toUpperCase(c1);
  char u2 = Character.toUpperCase(c2);
  if (u1 == u2) return true;
  return Character.toLowerCase(u1) == Character.toLowerCase(u2);
}



static String xltrim(String s) {
  int i = 0, n = l(s);
  while (i < n && contains(" \t\r\n", s.charAt(i)))
    ++i;
  return substr(s, i);
}


static boolean isLetterOrDigit(char c) {
  return Character.isLetterOrDigit(c);
}


// pred: char -> bool
static String takeCharsWhile(String s, Object pred) {
  int i = 0;
  while (i < l(s) && isTrue(callF(pred, s.charAt(i)))) ++i;
  return substring(s, 0, i);
}

static String takeCharsWhile(IF1<Character, Boolean> f, String s) {
  return takeCharsWhile(s, f);
}


static boolean isInstance(Class type, Object arg) {
  return type.isInstance(arg);
}




static <A extends Container> A addComponents(A c, Collection<? extends Component> components) {
  if (nempty(components)) { swing(() -> { 
    for (Component comp : components)
      if (comp != null)
        c.add(comp);
    revalidate(c);
  }); }
  return c;
}

static <A extends Container> A addComponents(A c, Component... components) {
  return addComponents(c, asList(components));
}


static double parseDouble(String s) {
  return empty(s) ? 0.0 : Double.parseDouble(s);
}


static String substr(String s, int x) {
  return substring(s, x);
}

static String substr(String s, int x, int y) {
  return substring(s, x, y);
}




static Object swing(Object f) {
  return swingAndWait(f);
}

static void swing(Runnable f) {
  swingAndWait(f);
}

static <A> A swing(F0<A> f) {
  return (A) swingAndWait(f);
}

static <A> A swing(IF0<A> f) {
  return (A) swingAndWait(f);
}


static <A extends Component> A revalidate(final A c) {
  if (c == null || !c.isShowing()) return c;
  { swing(() -> { 
    // magic combo to actually relayout and repaint
    c.revalidate();
    c.repaint();
  }); }
  return c;
}

static void revalidate(JFrame f) { revalidate((Component) f); }
static void revalidate(JInternalFrame f) { revalidate((Component) f); }




static void swingAndWait(Runnable r) { try {
  if (isAWTThread())
    r.run();
  else {
    r = addThreadInfoToRunnable(r);
    executingSwingCode(r);
    EventQueue.invokeAndWait(r);
  }
} catch (Exception __e) { throw rethrow(__e); } }

static Object swingAndWait(Object f) {
  if (isAWTThread())
    return callF(f);
  else {
    Var result = new Var();
    swingAndWait(new Runnable() {  public void run() { try { 
      result.set(callF(f));
    
} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "result.set(callF(f));"; }});
    return result.get();
  }
}




static Runnable addThreadInfoToRunnable(final Object r) {
  final Object info = _threadInfo();
  return info == null ? asRunnable(r) : new Runnable() {  public void run() { try {  _inheritThreadInfo(info); callF(r); 
} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "_inheritThreadInfo(info); callF(r);"; }};
}


//static event executingSwingCode(Runnable code);

static transient Set<IVF1<Runnable>> onExecutingSwingCode;
public static void onExecutingSwingCode(IVF1<Runnable> f) { onExecutingSwingCode = createOrAddToSyncLinkedHashSet(onExecutingSwingCode, f); }
public static void removeExecutingSwingCodeListener(IVF1<Runnable> f) { main.remove(onExecutingSwingCode, f); }
public static void executingSwingCode(Runnable code) {  if (onExecutingSwingCode != null) for (var listener : onExecutingSwingCode) pcallF_typed(listener, code); }




static List<VF1<Map>> _threadInfo_makers = synchroList();

static Object _threadInfo() {
  if (empty(_threadInfo_makers)) return null;
  HashMap map = new HashMap();
  pcallFAll(_threadInfo_makers, map);
  return map;
}


static Runnable asRunnable(Object o) {
  return toRunnable(o);
}




static void _inheritThreadInfo(Object info) {
  _threadInheritInfo(info);
}


static <A> Set<A> createOrAddToSyncLinkedHashSet(Set<A> set, A a) {
  if (set == null) set = syncLinkedHashSet();
  set.add(a);
  return set;
}


static Class main() {
  return getMainClass();
}


static <A> void remove(List<A> l, int i) {
  if (l != null && i >= 0 && i < l(l))
    l.remove(i);
}

static <A> void remove(Collection<A> l, A a) {
  if (l != null) l.remove(a);
}

static <A, B> B remove(Map<A, B> map, Object a) {
  return map == null ? null : map.remove(a);
}

static void remove(BitSet bs, int i) {
  bs.clear(i);
}



static <A> A pcallF_typed(F0<A> f) {
  try { return f == null ? null : f.get(); } catch (Throwable __e) { pcallFail(__e); } return null;
}



static <A, B> B pcallF_typed(F1<A, B> f, A a) {
  try { return f == null ? null : f.get(a); } catch (Throwable __e) { pcallFail(__e); } return null;
}



static <A> void pcallF_typed(VF1<A> f, A a) {
  try {
    { if (f != null) f.get(a); }
  } catch (Throwable __e) { pcallFail(__e); }
}


static <A> void pcallF_typed(IVF1<A> f, A a) {
  try {
    { if (f != null) f.get(a); }
  } catch (Throwable __e) { pcallFail(__e); }
}

static <A, B> void pcallF_typed(IVF2<A, B> f, A a, B b) {
  try {
    { if (f != null) f.get(a, b); }
  } catch (Throwable __e) { pcallFail(__e); }
}

static Object pcallF_typed(Runnable r) {
  try { { if (r != null) r.run(); } } catch (Throwable __e) { pcallFail(__e); } return null;
}

static <A> A pcallF_typed(IF0<A> f) {
  try { return f == null ? null : f.get(); } catch (Throwable __e) { pcallFail(__e); } return null;
}

static <A, B> B pcallF_typed(IF1<A, B> f, A a) {
  try { return f == null ? null : f.get(a); } catch (Throwable __e) { pcallFail(__e); } return null;
}





static Runnable toRunnable(final Object o) {
  if (o == null) return null;
  if (o instanceof Runnable) return (Runnable) o;
  
  if (o instanceof String) throw fail("callF_legacy");
  
  return new Runnable() {  public void run() { try {  callF(o) ;
} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "callF(o)"; }};
}


static List<VF1<Map>> _threadInheritInfo_retrievers = synchroList();

static void _threadInheritInfo(Object info) {
  if (info == null) return;
  pcallFAll(_threadInheritInfo_retrievers, (Map) info);
}


static <A> Set<A> syncLinkedHashSet() {
  return synchroLinkedHashSet();
}


static Class getMainClass() {
  return mc();
}

static Class getMainClass(Object o) { try {
  if (o == null) return null;
  if (o instanceof Class && eq(((Class) o).getName(), "x30")) return (Class) o;
  ClassLoader cl = (o instanceof Class ? (Class) o : o.getClass()).getClassLoader();
  if (cl == null) return null;
  String name = mainClassNameForClassLoader(cl);
  return loadClassFromClassLoader_orNull(cl, name);
} catch (Exception __e) { throw rethrow(__e); } }




// BREAKING CHANGE!
// Also NOTE: Iterators of these sync-wrapped collections
// after generally NOT thread-safe!
// TODO: change that?
static <A> Set<A> synchroLinkedHashSet() {
  
  
  return synchronizedSet(new CompactLinkedHashSet());
  
}


static Class loadClassFromClassLoader_orNull(ClassLoader cl, String name) {
  try {
    return cl == null ? null : cl.loadClass(name);
  } catch (ClassNotFoundException e) {
    return null;
  }
}




interface IImageRegions<Img extends WidthAndHeight> {
  public List<IImageRegion<Img>> regions();
  
  // for each pixel: region index (starting at 1)
  int[] regionMatrix();
  
  Img image();
  
  int nRegions();
  
  IImageRegion<Img> getRegion(int i);
}
static abstract class VF1<A> implements IVF1<A> {
  public abstract void get(A a);
}
// immutable, has strong refs
// Do not run in a synchronized block - it goes wrong in the presence
// of elaborate classloaders (like in Gazelle BEA)
// see #1102990 and #1102991

final static class _MethodCache {
  final Class c;
  final HashMap<String, List<Method>> cache = new HashMap();
  
  _MethodCache(Class c) {
  this.c = c; _init(); }
  
  void _init() {
    Class _c = c;
    java.lang.Module myModule = getClass().getModule();
    boolean anyHiddenClasses = false;
    
    while (_c != null) {
      boolean exported = classIsExportedTo(_c, myModule);
       
      
      if (!exported)
        anyHiddenClasses = true;
      else
        for (Method m : _c.getDeclaredMethods())
          if ((anyHiddenClasses || !isAbstract(m))
            && !reflection_isForbiddenMethod(m))
            multiMapPut(cache, m.getName(), makeAccessible(m));

      _c = _c.getSuperclass();
    }
    
    // add default methods - this might lead to a duplication
    // because the overridden method is also added, but it's not
    // a problem except for minimal performance loss.
    // If any classes in the hierarchy were inaccessible, we add
    // all interface methods (see test_callForbiddenMethodByReflection for a test)
    
    for (Class intf : allInterfacesImplementedBy(c))
      for (Method m : intf.getDeclaredMethods())
        if ((anyHiddenClasses || m.isDefault()) && !reflection_isForbiddenMethod(m))
          multiMapPut(cache, m.getName(), makeAccessible(m));

     
  }
  
  // Returns only matching methods
  Method findMethod(String method, Object[] args) { try {
    List<Method> m = cache.get(method);
     
    if (m == null) return null;
    int n = m.size();
    for (int i = 0; i < n; i++) {
      Method me = m.get(i);
      if (call_checkArgs(me, args, false))
        return me;
    }
    return null;
  } catch (Exception __e) { throw rethrow(__e); } }
  
  Method findStaticMethod(String method, Object[] args) { try {
    List<Method> m = cache.get(method);
    if (m == null) return null;
    int n = m.size();
    for (int i = 0; i < n; i++) {
      Method me = m.get(i);
      if (isStaticMethod(me) && call_checkArgs(me, args, false))
        return me;
    }
    return null;
  } catch (Exception __e) { throw rethrow(__e); } }
  
  //Cl<Method> allMethods() { ret allValues(cache); }
}
// Meta - a "minimal" approach to adding meta-level to Java objects

static class Meta implements IMeta {
  
// Meta - a "minimal" approach to adding meta-level to Java objects
// (implementing the interface IMeta)

// We allocate one extra field for each Java object to make it
// reasoning-compatible (reasoning-compatible = extensible with
// fields of any name at runtime).
//
// We couldn't go for 0 extra fields (meta values must be linked
// directly from the object) and there are no half fields in
// Java... so there you go.
//
// Also, if you don't use any meta data, you are probably not
// reasoning about anything. The point of reasoning in JavaX is
// to attach information to objects directly used in the program.

// Possible information contained in the meta field:
//   Origin, destination, security level, sender, cost center,
//   purpose, list of reifications, ...

// So here it is. THE FIELD YOU HAVE BEEN WAITING FOR!

// [We also have IMeta to retrofit foreign classes (rare but
// probably useful).]

//////////////////////
// The "meta" field //
//////////////////////

// Generic meta value of any kind, but the typical case is it's a
// Map with extra field values for the object etc.
// "meta" is volatile to avoid synchronization; but you can also synchronize on
// _tempMetaMutex() which is usually the object itself. Collections
// and maps are exempt from using the collections's monitor as the meta
// mutex because their monitor tends to be held for long operations
// (e.g. cloneList). For those we use a substantially more complex
// algorithm using a weakMap. Probably overkill. I may reconsider.

volatile Object meta;

// The meta field is not transient, thus by default it will be
// persisted like anything else unless you customize your object
// to suppress or modulate this.

// ...and the interface methods

public void _setMeta(Object meta) { this.meta = meta; }
public Object _getMeta() { return meta; }

// MOST functions are implemented in IMeta (default implementations)

// Scaffolding convenience functions

final boolean scaffolding(){ return scaffoldingEnabled(); }
final boolean scaffolded(){ return scaffoldingEnabled(); }
boolean scaffoldingEnabled() { return main.scaffoldingEnabled(this); }
boolean scaffoldingEnabled(Object o) { return main.scaffoldingEnabled(o); }

// Implementing setMetaToString

String toString_base() { return super.toString(); }
public String toString() {
  Object o = metaGet("toString", this);
  if (o instanceof String) return ((String) o);
  if (o instanceof IF1) return str(((IF1) o).get(this));
  return toString_base();
}
}
static class Matches {
  String[] m;
  
  Matches() {}
  Matches(String... m) {
  this.m = m;}
  
  String get(int i) { return i < m.length ? m[i] : null; }
  String unq(int i) { return unquote(get(i)); }
  
  String tlc(int i) { return unq(i).toLowerCase(); }
  boolean bool(int i) { return "true".equals(unq(i)); }
  String rest() { return m[m.length-1]; } // for matchStart
  int psi(int i) { return Integer.parseInt(unq(i)); }
  
  public String toString() { return "Matches(" + joinWithComma(quoteAll(asList(m))) + ")"; }
  
  public int hashCode() { return _hashCode(toList(m)); }
  public boolean equals(Object o) { return o instanceof Matches && arraysEqual(m, ((Matches) o).m); }
}

// for the version with MasterSymbol (used WAY back in "Smart Bot"!) see #1010608

static class Symbol implements CharSequence {
  String text;
  
  Symbol() {}
  Symbol(String text, boolean dummy) {
  this.text = text;} // weird signature to prevent accidental calling
  
  public int hashCode() { return _hashCode(text); }
  public String toString() { return text; }
  public boolean equals(Object o) {
    return this == o;
  }

  // implementation of CharSequence methods
  
  public int length() { return text.length(); }
  public char charAt(int index) { return text.charAt(index); }
  public CharSequence subSequence(int start, int end) {
    return text.substring(start, end);
  }
}
static class Var<A> implements IVar<A>, ISetter<A> {
  Var() {}
  Var(A v) {
  this.v = v;}

  
  
A v; // you can access this directly if you use one thread

public synchronized void set(A a) {
  if (v != a) {
    v = a;
    notifyAll();
  }
}

public synchronized A get() { return v; }
public synchronized boolean has() { return v != null; }
public void clear() { set(null); }

public synchronized A getAndSet(A a) {
  var value = v;
  set(a);
  return value;
}

public IF0<A> getter() { return () -> get(); }
public IVF1<A> setter() { return __39 -> set(__39); }
public String toString() { return str(this.get()); }
}
static interface IMeta {
  // see class "Meta" for the bla bla
  
  public void _setMeta(Object meta);
  public Object _getMeta();
  default public IAutoCloseableF0 _tempMetaMutex() {
    return new IAutoCloseableF0() {
      public Object get() { return IMeta.this; }
      public void close() {}
    };
  }
  
  // actually query another object
  default public Object getMeta(Object obj, Object key){ return metaGet(obj, key); }
default public Object metaGet(Object obj, Object key) {
    // call global function
    return metaMapGet(obj, key);
  }
  
  default public Object metaGet(String key, Object obj) {
    // call global function
    return metaMapGet(obj, key);
  }
  
  default public Object getMeta(Object key){ return metaGet(key); }
default public Object metaGet(Object key) {
    if (key == null) return null;
    Object meta = _getMeta();
    if (meta instanceof Map) return ((Map) meta).get(key);
    return null;
  }
  
  default public void metaSet(IMeta obj, Object key, Object value){ metaPut(obj, key, value); }
default public void metaPut(IMeta obj, Object key, Object value) {
    // call global function
    metaMapPut(obj, key, value);
  }
  
  default public void metaSet(Object key, Object value){ metaPut(key, value); }
default public void metaPut(Object key, Object value) {
    if (key == null) return;
    Map map = convertObjectMetaToMap(this);
    syncMapPutOrRemove(map, key, value);
  }
}
static class Scorer<A> {
  double score, total;
  List<A> successes, errors; // set to non-null if you want them filled
  boolean verboseFailures, verboseAll;
  
  final void add(double score){ addZeroToOne(score); }
void addZeroToOne(double score) {
    ++total;
    this.score += clamp(score, 0, 1);
  }
  
  void addZeroToOneError(double error) {
    addZeroToOne(1-error);
  }
  
  void addError() { add(false); }
  void addError(A info) { add(false, info); }
  void error(A info) { addError(info); }
  void addOK() { add(true); }
  void addOK(A info) { add(true, info); }
  void ok() { addOK(); }
  void ok(A info) { addOK(info); }
  
  boolean add(boolean correct) {
    ++total;
    if (correct) ++score;
    return correct;
  }
  
  boolean add(boolean correct, A info) {
    main.add(correct ? successes : errors, info);
    if (verboseAll || verboseFailures && !correct)
      _print((correct ? "[GOOD] " : "[BAD] ") + info);
    return add(correct);
  }
  
  // works if you use Scorer or Scorer<S>
  void eq(Object a, Object b) {
    if (_eq(a, b))
      add(true);
    else
      add(false, (A) (a + " != " + b));
  }
  
  void print() {
    main.print(toString());
  }
  
  public String toString() {
    return formatDouble(ratioToPercent(score, total), 1) + "% correct (n=" + formatDouble(total, 1) + ")";
  }
  
  double get() {
    return ratioToPercent(score, total);
  }
  
  double percentScore() { return get(); }
  double score() { return get(); }
  
  boolean allCorrect() {
    return score == total;
  }
  
  void add(Scorer scorer) {
    if (scorer == null) return;
    total += scorer.total;
    score += scorer.score;
    addAll(successes, scorer.successes);
    addAll(errors, scorer.errors);
  }
  
  void collectErrors() {
    errors = new ArrayList();
  }
  
  void collectSuccesses() {
    successes = new ArrayList();
  }
}

interface IImageRegion<Img extends WidthAndHeight> extends INumberOfPixels, IPixelSet {
  // REQUIRED METHODS
  
  // smallest rectangle that all of the region's pixels are contained in
  public Rect bounds();

  public IterableIterator<Pt> pixelIterator();
  public boolean contains(int x, int y);
  
  // OPTIONAL METHODS
  
  // get whole image that the region refers to
  public default Img image() { return null; }
  
  // which object made this
  public default Object creator() { return null; }
  
  public default int indexInCreator() { return 0; }
  
  // was diagonal walking enabled?
  public default Boolean createdWithDiagonals() { return null; }
  
  public default int nPixels(){ return numberOfPixels(); }
public default int numberOfPixels() { return l(pixelIterator()); }
  public default Pt firstPixel() { return first(pixelIterator()); }
  
  // gets the region's color (what exactly this means is defined
  // by the creator of this object)
  public default Color color() { return null; }
  
  public default int brightness() { return -1; }
  
  public default OnePathWithOrigin outline() {
    return g22_regionOutline(this);
  }
  
  default Image2B toImage2B() { return new RegionToImage2B(this).get(); }
  
  default int[] pixelsAsIntArray() { throw unimplemented(); }
  
  // CONVENIENCE/ORTHOGONALITY METHODS
  
  default IPixelSet pixelSet() { return this; }
}
// In the newest pinging system (with flag PingV3), a ping source
// is the object that "allows" some code to run.
// When that code calls ping(), the ping source's action (if defined)
// is triggered.

// This allows randomly interrupting code execution, for example.

static class PingSource {
  // returns true if it slept
   final public PingSource setAction(IF0<Boolean> action){ return action(action); }
public PingSource action(IF0<Boolean> action) { this.action = action; return this; }  final public IF0<Boolean> getAction(){ return action(); }
public IF0<Boolean> action() { return action; }
volatile IF0<Boolean> action;
  
  // optional description of this ping source
  String text;
  
  // optional thread pool that this ping source likes to run in
  ThreadPool threadPool;
  
  PingSource() {}
  PingSource(ThreadPool threadPool) {
  this.threadPool = threadPool;}
  PingSource(ThreadPool threadPool, String text) {
  this.text = text;
  this.threadPool = threadPool;}
  PingSource(IF0<Boolean> action) {
  this.action = action;}

  // returns true if it slept
  final boolean get() {
    var a = action;
    return a != null && a.get();
  }
  
  final void ping() { 
    var a = action;
    if (a != null) a.get();
  }
  
  void cancel() {
    action = new Cancelled();
  }
  
  class Cancelled implements IF0<Boolean> {
    public Boolean get() { throw new PingSourceCancelledException(PingSource.this); }
  }
  
  class Encapsulated implements Runnable , IFieldsToList{
  Runnable r;
  Encapsulated() {}
  Encapsulated(Runnable r) {
  this.r = r;}public Object[] _fieldsToList() { return new Object[] {r}; }

    public void run() { try {
      //System.out.println("Encapsulated running: " + r);
      try {
        pingSource_tl().set(PingSource.this);
        //System.out.println("Ping source set");
        ping();
        r.run();
        //System.out.println("Done running");
      } finally {
        //System.out.println("Finally");
        pingSource_tl().set(null);
      }
    } catch (Exception __e) { throw rethrow(__e); } }
    
    public String toString() { return PingSource.this + ": " + r; }
  }
  
  void dO(Runnable r) {
    if (r == null) return;
    threadPool.acquireThreadOrQueue(new Encapsulated(r));
  }
  
  public String toString() { String t = text; return nempty(t) ? t : super.toString(); }
  
  ISleeper_v2 sleeper() { return threadPool.sleeper(); }
}
// records its full size (total value count) in a field now
static class MultiMap<A,B> implements IMultiMap<A, B> {
  Map<A, List<B>> data = new HashMap<A, List<B>>();
  int fullSize;
  
  MultiMap() {}
  MultiMap(boolean useTreeMap) { if (useTreeMap) data = new TreeMap(); }
  MultiMap(MultiMap<A, B> map) { putAll(map); }
  MultiMap(Map<A, List<B>> data) {
  this.data = data;}

  void put(A key, B value) { synchronized(data) {
    List<B> list = data.get(key);
    if (list == null)
      data.put(key, list = _makeEmptyList());
    list.add(value);
    ++fullSize;
  }}

  void add(A key, B value) { put(key, value); }

  void addAll(A key, Collection<B> values) { putAll(key, values); }
  
  void addAllIfNotThere(A key, Collection<B> values) { synchronized(data) {
    for (B value : values)
      setPut(key, value);
  }}
  
  void setPut(A key, B value) { synchronized(data) {
    if (!containsPair(key, value))
      put(key, value);
  }}
  
  boolean containsPair(A key, B value) { synchronized(data) {
    return get(key).contains(value);
  }}
  
  void putAll(Collection<A> keys, B value) { synchronized(data) {
    for (A key : unnullForIteration(keys))
      put(key, value);
  }}

  void putAll(A key, Collection<B> values) { synchronized(data) {
    if (nempty(values)) getActual(key).addAll(values);
  }}

  void putAll(Iterable<Pair<A, B>> pairs) { synchronized(data) {
    for (Pair<A, B> p : unnullForIteration(pairs))
      put(p.a, p.b);
  }}
  
  void removeAll(A key, Collection<B> values) { synchronized(data) {
    for (B value : values)
      remove(key, value);
  }}
  
  public List<B> get(A key) { synchronized(data) {
    List<B> list = data.get(key);
    return list == null ? Collections.<B> emptyList() : list;
  }}
  
  List<B> getOpt(A key) { synchronized(data) {
    return data.get(key);
  }}

  List<B> getAndClear(A key) { synchronized(data) {
    List<B> l = cloneList(data.get(key));
    remove(key);
    return l;
  }}
  
  // returns actual mutable live list
  // creates the list if not there
  List<B> getActual(A key) { synchronized(data) {
    List<B> list = data.get(key);
    if (list == null)
      data.put(key, list = _makeEmptyList());
    return list;
  }}
 
  void clean(A key) { synchronized(data) {
    List<B> list = data.get(key);
    if (list != null && list.isEmpty()) {
      fullSize -= l(list);
      data.remove(key);
    }
  }}

  final public Set<A> keys(){ return keySet(); }
public Set<A> keySet() { synchronized(data) {
    return data.keySet();
  }}

  void remove(A key) { synchronized(data) {
    fullSize -= l(this.getOpt(key));
    data.remove(key);
  }}
  
  final void remove(Pair<A, B> p){ removePair(p); }
void removePair(Pair<A, B> p) {
    if (p != null) remove(p.a, p.b);
  }

  void remove(A key, B value) { synchronized(data) {
    List<B> list = data.get(key);
    if (list != null) {
      if (list.remove(value))
        fullSize--;
      if (list.isEmpty())
        data.remove(key);
    }
  }}

  void clear() { synchronized(data) {
    data.clear();
  }}

  boolean containsKey(A key) { synchronized(data) {
    return data.containsKey(key);
  }}

  B getFirst(A key) { synchronized(data) {
    List<B> list = get(key);
    return list.isEmpty() ? null : list.get(0);
  }}
  
  void addAll(MultiMap<A, B> map) { putAll(map); }
  
  void putAll(MultiMap<A, B> map) { synchronized(data) {
    for (A key : map.keySet())
      putAll(key, map.get(key));
  }}
  
  void putAll(Map<A, B> map) { synchronized(data) {
    if (map != null) for (Map.Entry<A, B> e : map.entrySet())
      put(e.getKey(), e.getValue());
  }}
  
  final public int keyCount(){ return keysSize(); }
public int keysSize() { synchronized(data) { return l(data); }}
  
  final public int fullSize(){ return size(); }
public int size() { synchronized(data) {
    return fullSize;
  }}
  
  // expensive operation
  List<A> reverseGet(B b) { synchronized(data) {
    List<A> l = new ArrayList();
    for (A key : data.keySet())
      if (data.get(key).contains(b))
        l.add(key);
    return l;
  }}
  
  Map<A, List<B>> asMap() { synchronized(data) {
    return cloneMap(data);
  }}
  
  boolean isEmpty() { synchronized(data) { return data.isEmpty(); }}
  
  // override in subclasses
  List<B> _makeEmptyList() {
    return new ArrayList();
  }
  
  // returns live lists
  Collection<List<B>> allLists() {
    synchronized(data) {
      return new ArrayList(data.values());
    }
  }
  Collection<List<B>> values() { return allLists(); }
  
  List<B> allValues() {
    return concatLists(data.values());
  }
  
  Object mutex() { return data; }
  
  public String toString() { return "mm" + str(data); }
  
  Map<A, List<B>> innerMap() { return data; }
}
// Note: This does have the values problem (complicated values can cause memory leaks)
static class BetterThreadLocal<A> {
  Map<Thread, A> map = newWeakHashMap();
  
  BetterThreadLocal() {}
  BetterThreadLocal(A value) { set(value); }
  
  boolean isSet() { return map.containsKey(currentThread()); }
  
  A get() {
    if (map.containsKey(currentThread()))
      return map.get(currentThread());
    A value = initialValue();
    set(value);
    return value;
  }
  
  A get(Thread thread) {
    return thread == null ? null : map.get(thread);
  }
  
  void set(A a) {
    map.put(currentThread(), a);
  }
  
  public A initialValue() { return null; }
}
interface IntSize {
  int size();
  
  default boolean isEmpty() { return size() == 0; }
}
/*
 * @(#)WeakHashMap.java 1.5 98/09/30
 *
 * Copyright 1998 by Sun Microsystems, Inc.,
 * 901 San Antonio Road, Palo Alto, California, 94303, U.S.A.
 * All rights reserved.
 *
 * This software is the confidential and proprietary information
 * of Sun Microsystems, Inc. ("Confidential Information").  You
 * shall not disclose such Confidential Information and shall use
 * it only in accordance with the terms of the license agreement
 * you entered into with Sun.
 */
 
// From https://github.com/mernst/plume-lib/blob/df0bfafc3c16848d88f4ea0ef3c8bf3367ae085e/java/src/plume/WeakHasherMap.java

static final class WeakHasherMap<K,V> extends AbstractMap<K,V> implements Map<K,V> {

    private Hasher hasher = null;
    /*@Pure*/
    private boolean keyEquals(Object k1, Object k2) {
  return (hasher==null ? k1.equals(k2)
           : hasher.equals(k1, k2));
    }
    /*@Pure*/
    private int keyHashCode(Object k1) {
  return (hasher==null ? k1.hashCode()
           : hasher.hashCode(k1));
    }

    // The WeakKey class can't be static because it depends on the hasher.
    // That in turn means that its methods can't be static.
    // However, I need to be able to call the methods such as create() that
    // were static in the original version of this code.
    // This finesses that.

    private /*@Nullable*/ WeakKey WeakKeyCreate(K k) {
  if (k == null) return null;
  else return new WeakKey(k);
    }
    private /*@Nullable*/ WeakKey WeakKeyCreate(K k, ReferenceQueue<? super K> q) {
  if (k == null) return null;
  else return new WeakKey(k, q);
    }

    // Cannot be a static class: uses keyHashCode() and keyEquals()
    private final class WeakKey extends WeakReference<K> {
  private int hash; /* Hashcode of key, stored here since the key
           may be tossed by the GC */

  private WeakKey(K k) {
      super(k);
      hash = keyHashCode(k);
  }

  private /*@Nullable*/ WeakKey create(K k) {
      if (k == null) return null;
      else return new WeakKey(k);
  }

  private WeakKey(K k, ReferenceQueue<? super K> q) {
      super(k, q);
      hash = keyHashCode(k);
  }

  private /*@Nullable*/ WeakKey create(K k, ReferenceQueue<? super K> q) {
      if (k == null) return null;
      else return new WeakKey(k, q);
  }

        /* A WeakKey is equal to another WeakKey iff they both refer to objects
     that are, in turn, equal according to their own equals methods */
  /*@Pure*/
  @Override
  public boolean equals(/*@Nullable*/ Object o) {
            if (o == null) return false; // never happens
      if (this == o) return true;
            // This test is illegal because WeakKey is a generic type,
            // so use the getClass hack below instead.
      // if (!(o instanceof WeakKey)) return false;
            if (!(o.getClass().equals(WeakKey.class))) return false;
      Object t = this.get();
            @SuppressWarnings("unchecked")
      Object u = ((WeakKey)o).get();
      if ((t == null) || (u == null)) return false;
      if (t == u) return true;
      return keyEquals(t, u);
  }

  /*@Pure*/
  @Override
  public int hashCode() {
      return hash;
  }

    }


    /* Hash table mapping WeakKeys to values */
    private HashMap<WeakKey,V> hash;

    /* Reference queue for cleared WeakKeys */
    private ReferenceQueue<? super K> queue = new ReferenceQueue<K>();


    /* Remove all invalidated entries from the map, that is, remove all entries
       whose keys have been discarded.  This method should be invoked once by
       each public mutator in this class.  We don't invoke this method in
       public accessors because that can lead to surprising
       ConcurrentModificationExceptions. */
    @SuppressWarnings("unchecked")
    private void processQueue() {
  WeakKey wk;
  while ((wk = (WeakKey)queue.poll()) != null) { // unchecked cast
      hash.remove(wk);
  }
    }


    /* -- Constructors -- */

    /**
     * Constructs a new, empty <code>WeakHashMap</code> with the given
     * initial capacity and the given load factor.
     *
     * @param  initialCapacity  the initial capacity of the
     *                          <code>WeakHashMap</code>
     *
     * @param  loadFactor       the load factor of the <code>WeakHashMap</code>
     *
     * @throws IllegalArgumentException  If the initial capacity is less than
     *                                   zero, or if the load factor is
     *                                   nonpositive
     */
    public WeakHasherMap(int initialCapacity, float loadFactor) {
  hash = new HashMap<WeakKey,V>(initialCapacity, loadFactor);
    }

    /**
     * Constructs a new, empty <code>WeakHashMap</code> with the given
     * initial capacity and the default load factor, which is
     * <code>0.75</code>.
     *
     * @param  initialCapacity  the initial capacity of the
     *                          <code>WeakHashMap</code>
     *
     * @throws IllegalArgumentException  If the initial capacity is less than
     *                                   zero
     */
    public WeakHasherMap(int initialCapacity) {
  hash = new HashMap<WeakKey,V>(initialCapacity);
    }

    /**
     * Constructs a new, empty <code>WeakHashMap</code> with the default
     * capacity and the default load factor, which is <code>0.75</code>.
     */
    public WeakHasherMap() {
  hash = new HashMap<WeakKey,V>();
    }

    /**
     * Constructs a new, empty <code>WeakHashMap</code> with the default
     * capacity and the default load factor, which is <code>0.75</code>.
     * The <code>WeakHashMap</code> uses the specified hasher for hashing
     * keys and comparing them for equality.
     * @param h the Hasher to use when hashing values for this map
     */
    public WeakHasherMap(Hasher h) {
  hash = new HashMap<WeakKey,V>();
  hasher = h;
    }


    /* -- Simple queries -- */

    /**
     * Returns the number of key-value mappings in this map.
     * <strong>Note:</strong> <em>In contrast to most implementations of the
     * <code>Map</code> interface, the time required by this operation is
     * linear in the size of the map.</em>
     */
    /*@Pure*/
    @Override
    public int size() {
  return entrySet().size();
    }

    /**
     * Returns <code>true</code> if this map contains no key-value mappings.
     */
    /*@Pure*/
    @Override
    public boolean isEmpty() {
  return entrySet().isEmpty();
    }

    /**
     * Returns <code>true</code> if this map contains a mapping for the
     * specified key.
     *
     * @param   key   the key whose presence in this map is to be tested
     */
    /*@Pure*/
    @Override
    public boolean containsKey(Object key) {
        @SuppressWarnings("unchecked")
        K kkey = (K) key;
  return hash.containsKey(WeakKeyCreate(kkey));
    }


    /* -- Lookup and modification operations -- */

    /**
     * Returns the value to which this map maps the specified <code>key</code>.
     * If this map does not contain a value for this key, then return
     * <code>null</code>.
     *
     * @param  key  the key whose associated value, if any, is to be returned
     */
    /*@Pure*/
    @Override
    public /*@Nullable*/ V get(Object key) {  // type of argument is Object, not K
        @SuppressWarnings("unchecked")
        K kkey = (K) key;
  return hash.get(WeakKeyCreate(kkey));
    }

    /**
     * Updates this map so that the given <code>key</code> maps to the given
     * <code>value</code>.  If the map previously contained a mapping for
     * <code>key</code> then that mapping is replaced and the previous value is
     * returned.
     *
     * @param  key    the key that is to be mapped to the given
     *                <code>value</code>
     * @param  value  the value to which the given <code>key</code> is to be
     *                mapped
     *
     * @return  the previous value to which this key was mapped, or
     *          <code>null</code> if if there was no mapping for the key
     */
    @Override
    public V put(K key, V value) {
  processQueue();
  return hash.put(WeakKeyCreate(key, queue), value);
    }

    /**
     * Removes the mapping for the given <code>key</code> from this map, if
     * present.
     *
     * @param  key  the key whose mapping is to be removed
     *
     * @return  the value to which this key was mapped, or <code>null</code> if
     *          there was no mapping for the key
     */
    @Override
    public V remove(Object key) { // type of argument is Object, not K
  processQueue();
        @SuppressWarnings("unchecked")
        K kkey = (K) key;
  return hash.remove(WeakKeyCreate(kkey));
    }

    /**
     * Removes all mappings from this map.
     */
    @Override
    public void clear() {
  processQueue();
  hash.clear();
    }


    /* -- Views -- */


    /* Internal class for entries */
    // This can't be static, again because of dependence on hasher.
    @SuppressWarnings("TypeParameterShadowing")
    private final class Entry<K,V> implements Map.Entry<K,V> {
  private Map.Entry<WeakKey,V> ent;
  private K key;  /* Strong reference to key, so that the GC
           will leave it alone as long as this Entry
           exists */

  Entry(Map.Entry<WeakKey,V> ent, K key) {
      this.ent = ent;
      this.key = key;
  }

  /*@Pure*/
  @Override
  public K getKey() {
      return key;
  }

  /*@Pure*/
  @Override
  public V getValue() {
      return ent.getValue();
  }

  @Override
  public V setValue(V value) {
      return ent.setValue(value);
  }

        /*@Pure*/
        private boolean keyvalEquals(K o1, K o2) {
      return (o1 == null) ? (o2 == null) : keyEquals(o1, o2);
  }

        /*@Pure*/
        private boolean valEquals(V o1, V o2) {
      return (o1 == null) ? (o2 == null) : o1.equals(o2);
  }

        /*@Pure*/
        @SuppressWarnings("NonOverridingEquals")
        public boolean equals(Map.Entry<K,V> e /* Object o*/) {
            // if (! (o instanceof Map.Entry)) return false;
            // Map.Entry<K,V> e = (Map.Entry<K,V>)o;
      return (keyvalEquals(key, e.getKey())
        && valEquals(getValue(), e.getValue()));
  }

  /*@Pure*/
  @Override
  public int hashCode() {
      V v;
      return (((key == null) ? 0 : keyHashCode(key))
        ^ (((v = getValue()) == null) ? 0 : v.hashCode()));
  }

    }


    /* Internal class for entry sets */
    private final class EntrySet extends AbstractSet<Map.Entry<K,V>> {
  Set<Map.Entry<WeakKey,V>> hashEntrySet = hash.entrySet();

  @Override
  public Iterator<Map.Entry<K,V>> iterator() {

      return new Iterator<Map.Entry<K,V>>() {
    Iterator<Map.Entry<WeakKey,V>> hashIterator = hashEntrySet.iterator();
    Map.Entry<K,V> next = null;

    @Override
    public boolean hasNext() {
        while (hashIterator.hasNext()) {
      Map.Entry<WeakKey,V> ent = hashIterator.next();
      WeakKey wk = ent.getKey();
      K k = null;
      if ((wk != null) && ((k = wk.get()) == null)) {
          /* Weak key has been cleared by GC */
          continue;
      }
      next = new Entry<K,V>(ent, k);
      return true;
        }
        return false;
    }

    @Override
    public Map.Entry<K,V> next() {
        if ((next == null) && !hasNext())
      throw new NoSuchElementException();
        Map.Entry<K,V> e = next;
        next = null;
        return e;
    }

    @Override
    public void remove() {
        hashIterator.remove();
    }

      };
  }

  /*@Pure*/
  @Override
  public boolean isEmpty() {
      return !(iterator().hasNext());
  }

  /*@Pure*/
  @Override
  public int size() {
      int j = 0;
      for (Iterator<Map.Entry<K,V>> i = iterator(); i.hasNext(); i.next()) j++;
      return j;
  }

  @Override
  public boolean remove(Object o) {
      processQueue();
      if (!(o instanceof Map.Entry<?,?>)) return false;
            @SuppressWarnings("unchecked")
      Map.Entry<K,V> e = (Map.Entry<K,V>)o; // unchecked cast
      Object ev = e.getValue();
      WeakKey wk = WeakKeyCreate(e.getKey());
      Object hv = hash.get(wk);
      if ((hv == null)
    ? ((ev == null) && hash.containsKey(wk)) : hv.equals(ev)) {
    hash.remove(wk);
    return true;
      }
      return false;
  }

  /*@Pure*/
  @Override
  public int hashCode() {
      int h = 0;
      for (Iterator<Map.Entry<WeakKey,V>> i = hashEntrySet.iterator(); i.hasNext(); ) {
    Map.Entry<WeakKey,V> ent = i.next();
    WeakKey wk = ent.getKey();
    Object v;
    if (wk == null) continue;
    h += (wk.hashCode()
          ^ (((v = ent.getValue()) == null) ? 0 : v.hashCode()));
      }
      return h;
  }

    }


    private /*@Nullable*/ Set<Map.Entry<K,V>> entrySet = null;

    /**
     * Returns a <code>Set</code> view of the mappings in this map.
     */
    /*@SideEffectFree*/
    @Override
    public Set<Map.Entry<K,V>> entrySet() {
  if (entrySet == null) entrySet = new EntrySet();
  return entrySet;
    }

    // find matching key
    K findKey(Object key) {
      processQueue();
      K kkey = (K) key;
      // TODO: use replacement for HashMap to avoid reflection
      WeakKey wkey = WeakKeyCreate(kkey);
      WeakKey found = hashMap_findKey(hash, wkey);
      return found == null ? null : found.get();
    }
}
static interface IF2_IntInt_Double {
  double get(int a, int b);
}
// -has fast nextElement() and prevElement()
// -design allows for more functions like reordering the list
// -Saves up to 34% in space over LinkedHashSet
//    (e.g. 22% for a set of 1,000 Ints)
static class CompactLinkedHashSet<A> extends AbstractSet<A> {
  UnsynchronizedCompactHashSet<Entry<A>> entries = new UnsynchronizedCompactHashSet();
  Entry<A> head, tail;
  
  static class Entry<A> {
    A value;
    Entry<A> prev, next;
    
    public int hashCode() {
      return _hashCode(value);
    }
    
    // "magic" equals function for CompactHashSet lookup without temp object
    public boolean equals(Object o) {
      return o == this || eq(value, o);
    }
  }
  
  public boolean add(A a) {
    if (entries.contains(a)) return false;
    Entry<A> n = new Entry();
    n.value = a;
    n.prev = tail;
    if (tail != null) tail.next = n;
    tail = n;
    if (head == null) head = n;
    entries.add(n);
    return true;
  }
  
  public boolean remove(Object a) {
    return remove(entries.find(a));
  }
  
  public boolean remove(Entry<A> node) {
    if (node == null) return false;
    if (node.next != null) node.next.prev = node.prev; else tail = node.prev;
    if (node.prev != null) node.prev.next = node.next; else head = node.next;
    entries.remove(node);
    return true;
  }
  
  public int size() { return entries.size(); }
  
  public IterableIterator<A> iterator() {
    return new IterableIterator<A>() {
      Entry<A> entry = head, prev = null;
      public boolean hasNext() { return entry != null; }
      public A next() {
        A a = entry.value;
        prev = entry;
        entry = entry.next;
        return a;
      }
      
      // untested
      public void remove() {
        if (prev == null) throw new IllegalStateException();
        CompactLinkedHashSet.this.remove(prev);
        prev = null;
      }
    };
  }
  
  public void clear() {
    entries.clear();
    head = tail = null;
  }
  
  public boolean contains(Object a) {
    return entries.contains(a);
  }
  
  public A find(Object o) {
    Entry<A> e = entries.find(o);
    return e == null ? null : e.value;
  }
  
  public A prevElement(A a) {
    Entry<A> e = entries.find(a);
    if (e == null || e.prev == null) return null;
    return e.prev.value;
  }
  
  public A nextElement(A a) {
    Entry<A> e = entries.find(a);
    if (e == null || e.next == null) return null;
    return e.next.value;
  }
  
  public A first() { return head == null ? null : head.value; }
  public A last() { return tail == null ? null : tail.value; }
  
  boolean removeIfSame(Object o) {
    A value = find(o);
    if (value == o) {
      remove(value);
      return true;
    }
    return false;
  }
}
static class Pair<A, B> implements Comparable<Pair<A, B>> {
   final public Pair<A, B> setA(A a){ return a(a); }
public Pair<A, B> a(A a) { this.a = a; return this; }  final public A getA(){ return a(); }
public A a() { return a; }
 A a;
   final public Pair<A, B> setB(B b){ return b(b); }
public Pair<A, B> b(B b) { this.b = b; return this; }  final public B getB(){ return b(); }
public B b() { return b; }
 B b;

  Pair() {}
  Pair(A a, B b) {
  this.b = b;
  this.a = a;}
  
  public int hashCode() {
    return hashCodeFor(a) + 2*hashCodeFor(b);
  }
  
  public boolean equals(Object o) {
    if (o == this) return true;
    if (!(o instanceof Pair)) return false;
    Pair t = (Pair) o;
    return eq(a, t.a) && eq(b, t.b);
  }
  
  public String toString() {
    return "<" + a + ", " + b + ">";
  }
  
  public int compareTo(Pair<A, B> p) {
    if (p == null) return 1;
    int i = ((Comparable<A>) a).compareTo(p.a);
    if (i != 0) return i;
    return ((Comparable<B>) b).compareTo(p.b);
  }
}
static class Fail extends RuntimeException implements IFieldsToList{
  Object[] objects;
  Fail() {}
  Fail(Object... objects) {
  this.objects = objects;}public Object[] _fieldsToList() { return new Object[] {objects}; }

  Fail(Throwable cause, Object... objects) {
    super(cause);
  this.objects = objects;
  }
  
  public String toString() { return joinNemptiesWithColon("Fail", getMessage()); }
  
  public String getMessage() { return commaCombine(getCause(), objects); }
}
static class Rect implements WidthAndHeight , IFieldsToList{
  static final String _fieldOrder = "x y w h";
  int x;
  int y;
  int w;
  int h;
  Rect() {}
  Rect(int x, int y, int w, int h) {
  this.h = h;
  this.w = w;
  this.y = y;
  this.x = x;}

public boolean equals(Object o) {
if (!(o instanceof Rect)) return false;
    Rect __1 =  (Rect) o;
    return x == __1.x && y == __1.y && w == __1.w && h == __1.h;
}

  public int hashCode() {
    int h = 2543108;
    h = boostHashCombine(h, _hashCode(x));
    h = boostHashCombine(h, _hashCode(y));
    h = boostHashCombine(h, _hashCode(w));
    h = boostHashCombine(h, _hashCode(h));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {x, y, w, h}; }

  Rect(Rectangle r) {
    x = r.x;
    y = r.y;
    w = r.width;
    h = r.height;
  }
  
  Rect(Pt p, int w, int h) {
  this.h = h;
  this.w = w; x = p.x; y = p.y; }
  Rect(Rect r) { x = r.x; y = r.y; w = r.w; h = r.h; }
  
  final Rectangle getRectangle() {
    return new Rectangle(x, y, w, h);
  }
  
  public String toString() {
    return x + "," + y + " / " + w + "," + h;
  }
  
  final int x1() { return x; }
  final int y1() { return y; }
  final int x2() { return x + w; }
  final int y2() { return y + h; }
  
  final boolean contains(Pt p) {
    return contains(p.x, p.y);
  }
  
  final boolean contains(int _x, int _y) {
    return _x >= x && _y >= y && _x < x+w && _y < y+h;
  }
  
  final boolean contains(Rectangle r) {
    return rectContains(this, r);
  }
  
  final boolean empty() { return w <= 0 || h <= 0; }
  
  final public int getWidth() { return w; }
  final public int getHeight() { return h; }
  
  final public int area() { return w*h; }
  
  final public int x() { return x; }
  final public int y() { return y; }
  
  WidthAndHeight widthAndHeight() { return main.widthAndHeight(w, h); }
}

static interface IBWImage extends MakesBufferedImage, IRGBImage {
  float getFloatPixel(int x, int y); // usually between 0 and 1
  
  default int getInt(int x, int y) { return iround(getFloatPixel(x, y)*255f); }
  
  // implementing IRGBImage
  default int getIntPixel(int x, int y) { return rgbIntFromGrayscale(getInt(x, y)); }
  
  default float getFloatPixel(Pt p) { return getFloatPixel(p.x, p.y); }
  
  default float getFloatPixel(int index) {
    int w = w();
    return getFloatPixel(index % w, index / w);
  }
  
  default float[] toFloatArray() {
    float[] data = new float[w()*h()];
    for (int i = 0; i < l(data); i++)
      data[i] = getFloatPixel(i);
    return data;
  }
  
  public default BufferedImage getBufferedImage() {
    return grayImageFromIBWImage(this);
  }
  
  default BWImage toBWImage() {
    return this instanceof BWImage ? (BWImage) this : iBWImageToBWImage(this);
  }
}
static class Pt implements Comparable<Pt>, IDoublePt {
  int x, y;
  
  Pt() {}
  Pt(Point p) {
    x = p.x;
    y = p.y;
  }
  Pt(int x, int y) {
  this.y = y;
  this.x = x;}
  
  Point getPoint() {
    return new Point(x, y);
  }
  
  public boolean equals(Object o) {
    return o instanceof Pt && x == ((Pt) o).x && y == ((Pt) o).y;
  }
  
  public int hashCode() {
    return boostHashCombine(x, y);
  }
  
  // compare in scan order
  public int compareTo(Pt p) {
    if (y != p.y) return cmp(y, p.y);
    return cmp(x, p.x);
  }
  
  public String toString() {
    return x + ", " + y;
  }
  
  double length() { return sqrt(x*x+y*y); }
  
  public Pt minus(Pt p) { return ptMinus(this, p); }
  
  public double x_double() { return x; }
  public double y_double() { return y; }
}
static abstract class F0<A> {
  abstract A get();
}
static abstract class F1<A, B> {
  abstract B get(A a);
}
// you still need to implement hasNext() and next()
static abstract class IterableIterator<A> implements Iterator<A>, Iterable<A> {
  public Iterator<A> iterator() {
    return this;
  }
  
  public void remove() {
    unsupportedOperation();
  }
}
abstract static class RandomAccessAbstractList<A> extends AbstractList<A> implements RandomAccess {
}
static class RGB {
  // usually in range [0, 1]
  public float r, g, b; // can't be final cause persistence
  
  RGB() {}
  
  public RGB(float brightness) {
    r = g = b = brightness;
  }
  
  public RGB(float r, float g, float b) {
    this.r = r;
    this.g = g;
    this.b = b;
  }

  public RGB(double r, double g, double b) {
    this.r = (float) r;
    this.g = (float) g;
    this.b = (float) b;
  }
  
  public RGB(double[] rgb) {
    this(rgb[0], rgb[1], rgb[2]);
  }

  public RGB(int rgb) {
    r = rgbRed(rgb)/255f;
    g = rgbGreen(rgb)/255f;
    b = rgbBlue(rgb)/255f;
  }
  
  public RGB(double brightness) {
    this((float) brightness);
  }

  public RGB(Color color) {
    r = color.getRed()/255f;
    g = color.getGreen()/255f;
    b = color.getBlue()/255f;
  }

  // TODO: 3-char version
  public RGB(String hex) {
    int i = l(hex)-6;
    r = Integer.parseInt(hex.substring(i, i+2), 16)/255f;
    g = Integer.parseInt(hex.substring(i+2, i+4), 16)/255f;
    b = Integer.parseInt(hex.substring(i+4, i+6), 16)/255f;
  }

  public float getComponent(int i) {
    return i == 0 ? r : i == 1 ? g : b;
  }

  public int getInt(int i) {
    return i == 0 ? redInt() : i == 1 ? greenInt() : blueInt();
  }
  
  public Color getColor() {
    return new Color(clampZeroToOne(r), clampZeroToOne(g), clampZeroToOne(b));
  }

  public static RGB newSafe(float r, float g, float b) {
    return new RGB(Math.max(0, Math.min(1, r)), Math.max(0, Math.min(1, g)), Math.max(0, Math.min(1, b)));
  }

  int asInt() { return getColor().getRGB() & 0xFFFFFF; }
  int getInt() { return getColor().getRGB() & 0xFFFFFF; }
  int asIntWithAlpha() { return rgbInt(redInt(), greenInt(), blueInt()) | 0xFF000000; }

  final public float brightness(){ return getBrightness(); }
public float getBrightness() {
    return (r+g+b)/3.0f;
  }

  public String getHexString() {
    return Integer.toHexString(asInt() | 0xFF000000).substring(2).toUpperCase();
  }

  @Override
  public boolean equals(Object o) {
    if (this == o) return true;
    if (!(o instanceof RGB)) return false;

    RGB rgb = (RGB) o;

    if (Float.compare(rgb.b, b) != 0) return false;
    if (Float.compare(rgb.g, g) != 0) return false;
    if (Float.compare(rgb.r, r) != 0) return false;

    return true;
  }

  @Override
  public int hashCode() {
    int result = (r != +0.0f ? Float.floatToIntBits(r) : 0);
    result = 31 * result + (g != +0.0f ? Float.floatToIntBits(g) : 0);
    result = 31 * result + (b != +0.0f ? Float.floatToIntBits(b) : 0);
    return result;
  }

  public boolean isBlack() {
    return r == 0f && g == 0f && b == 0f;
  }

  public boolean isWhite() {
    return r == 1f && g == 1f && b == 1f;
  }
  
  // This is hyperprecise
  boolean isGrayscale() {
    return r == g && g == b;
  }

  public String toString() {
    //return getHexString();
    return isGrayscale() ? formatChannel(r)
      : spaceCombine("RGB", formatChannel(r), formatChannel(g), formatChannel(b));
  }
  
  String formatChannel(float value) {
    return formatDouble(value, 2);
  }
  
  int redInt() { return iround(r*255); }
  int greenInt() { return iround(g*255); }
  int blueInt() { return iround(b*255); }
  
  static float brightnessToFloat(int brightness) { return brightness/255f; }
  
  RGB cloneMe() { return new RGB(r, g, b); }
}
interface PCallPolicy {
  void handlePcallFail(Throwable e);
}
public static interface IF0<A> {
  A get();
}
static interface Hasher<A> {
  int hashCode(A a);
  boolean equals(A a, A b);
}

static interface IFieldsToList {
  Object[] _fieldsToList();
}
static interface IF2<A, B, C> {
  C get(A a, B b);
}
static interface IF1<A, B> {
  B get(A a);
}
static class IntBuffer implements Iterable<Integer> {
  int[] data;
  int size;
  
  IntBuffer() {}
  IntBuffer(int size) { if (size != 0) data = new int[size]; }
  IntBuffer(Iterable<Integer> l) {
    if (l instanceof Collection) allocate(((Collection) l).size());
    addAll(l);
  }
  
  void add(int i) {
    if (size >= lIntArray(data)) {
      data = resizeIntArray(data, Math.max(1, toInt(Math.min(maximumSafeArraySize(), lIntArray(data)*2L))));
      if (size >= data.length) throw fail("IntBuffer too large: " + size);
    }
    data[size++] = i;
  }
  
  void allocate(int n) {
    data = resizeIntArray(data, max(n, size()));
  }
  
  void setSize(int n) {
    data = resizeIntArray(data, n);
    size = min(l(data), size);
  }
  
  void addAll(Iterable<Integer> l) {
    if (l != null) for (int i : l) add(i);
  }
  
  void addAll(int... l) {
    if (l != null) for (int i : l) add(i);
  }
  
  // Note: may return the internal array
  final int[] toIntArray(){ return toArray(); }
int[] toArray() {
    return size == 0 ? null : resizeIntArray(data, size);
  }
  
  int[] subArray(int from, int to) {
    return subIntArray(data, from, min(to, size));
  }
  
  int[] toArrayNonNull() {
    return unnull(toArray());
  }
  
  // abandoned version
  /*L<Int> toList() {
    ret intArrayToList(data, 0, size);
  }*/

  // now all these return a virtual list
  final List<Integer> asList(){ return toList(); }
final List<Integer> asVirtualList(){ return toList(); }
List<Integer> toList() {
    return new RandomAccessAbstractList<Integer>() {
      public int size() { return size; }
      public Integer get(int i) { return IntBuffer.this.get(i); }
      public Integer set(int i, Integer val) {
        Integer a = get(i);
        data[i] = val;
        return a;
      }
    };
  }
  
  void reset() { size = 0; }
  void clear() { reset(); }
  
  int size() { return size; }
  boolean isEmpty() { return size == 0; }
  
  int get(int idx) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    return data[idx];
  }
  
  void set(int idx, int value) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    data[idx] = value;
  }
  
  int popLast() {
    if (size == 0) throw fail("empty buffer");
    return data[--size];
  }
  
  int last() { return data[size-1]; }
  int nextToLast() { return data[size-2]; }
  
  public String toString() { return squareBracket(joinWithSpace(toList())); }
  
  public Iterator<Integer> iterator() {
    return new IterableIterator<Integer>() {
      int i = 0;
      
      public boolean hasNext() { return i < size; }
      public Integer next() {
        //if (!hasNext()) fail("Index out of bounds: " + i);
        return data[i++];
      }
    };
  }
  
  public IntegerIterator integerIterator() {
    return new IntegerIterator() {
      int i = 0;
      
      public boolean hasNext() { return i < size; }
      public int next() {
        //if (!hasNext()) fail("Index out of bounds: " + i);
        return data[i++];
      }
      public String toString() { return "Iterator@" + i + " over " + IntBuffer.this; }
    };
  }
  
  void trimToSize() {
    data = resizeIntArray(data, size);
  }
}
// TODO: subclass RuntimeException and use Meta instead of DynamicObject
static class PersistableThrowable extends DynamicObject {
  String className;
  String msg;
  String stacktrace;
   final public PersistableThrowable setActualThrowable(Throwable actualThrowable){ return actualThrowable(actualThrowable); }
public PersistableThrowable actualThrowable(Throwable actualThrowable) { this.actualThrowable = actualThrowable; return this; }  final public Throwable getActualThrowable(){ return actualThrowable(); }
public Throwable actualThrowable() { return actualThrowable; }
transient Throwable actualThrowable;
  
  PersistableThrowable() {}
  PersistableThrowable(Throwable e) {
    actualThrowable = e;
    if (e == null)
      className = "Crazy Null Error";
    else {
      className = getClassName(e).replace('/', '.');
      msg = e.getMessage();
      stacktrace = getStackTrace_noRecord(e);
    }
  }
  
  public String toString() {
    return nempty(msg) ? className + ": " + msg : className;
  }
  
  RuntimeException asRuntimeException() {
    if (actualThrowable != null)
      return main.asRuntimeException(actualThrowable);
    return new Fail(this);
  }
}
static interface IVF1<A> {
  void get(A a);
}
static interface IVF2<A, B> {
  void get(A a, B b);
}
static interface WidthAndHeight {
  default int w(){ return getWidth(); }
default int width(){ return getWidth(); }
int getWidth();
  default int h(){ return getHeight(); }
default int height(){ return getHeight(); }
int getHeight();
  
  public default Rect bounds() { return rect(0, 0, getWidth(), getHeight()); }
  
  default int area() { return toInt(areaAsLong()); }
  default long areaAsLong() { return longMul(w(), h()); }
}


abstract static class AbstractMatrix<A> implements Matrix<A> {
  AbstractMatrix() {}
  int w, h;

  AbstractMatrix(int w, int h) {
  this.h = h;
  this.w = w;}

  public int getWidth() { return w; }
  public int getHeight() { return h; }
  
  public String toString() {
    return flexLines(
      roundBracket(w+"x"+h),
      countIteratorToList(y -> str(getLine(y)), getHeight()));
  }
  
  public void set(int x, int y, A a) { throw unimplemented(); }
}
static interface IRGBImage extends MakesBufferedImage {
  int getIntPixel(int x, int y);
}
static class PingSourceCancelledException extends RuntimeException implements IFieldsToList{
  PingSource pingSource;
  PingSourceCancelledException() {}
  PingSourceCancelledException(PingSource pingSource) {
  this.pingSource = pingSource;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + pingSource + ")"; }public Object[] _fieldsToList() { return new Object[] {pingSource}; }

}
static class Image2B implements IBinaryImage {
  Image2B() {}
  int w, h;
  byte[] pixels;
  
  Image2B(int w, int h, byte[] pixels) {
  this.pixels = pixels;
  this.h = h;
  this.w = w; cleanPixelArray(); }
  
  Image2B(Image2B img) {
    w = img.getWidth();
    h = img.getHeight();
    pixels = cloneByteArray(img.pixels);
  }
  
  Image2B(RGBImage img) {
    w = img.getWidth();
    h = img.getHeight();
    pixels = new byte[(w*h+7)/8];
    for (int y = 0; y < h; y++) for (int x = 0; x < w; x++)
      if (img.getPixel(x, y).getBrightness() >= 0.5f) {
        int i = y*w+x;
        pixels[i/8] |= 1 << (i & 7);
      }
  }
  
  Image2B(BWImage img) {
    this(img, 128);
  }
  
  // >= threshold
  Image2B(BWImage img, int threshold) {
    w = img.w(); h = img.h();
    int n = w*h;
    int nOut = (n+7)/8;
    byte[] pixels = this.pixels = new byte[nOut];
    byte[] bwPixels = img.pixels;
    int iIn = 0;
    
    // do the bulk
    for (int iOut = 0; iOut < nOut-1; iOut++) {
      int value = 0;
      for (int bit = 0; bit < 8; bit++) {
        value >>= 1;
        if (ubyteToInt(bwPixels[iIn++]) >= threshold)
          value |= 0x80;
      }
      pixels[iOut] = (byte) value;
    }
    
    // do last (up to 7) bits
    for (; iIn < n; iIn++)
      if (ubyteToInt(bwPixels[iIn]) >= threshold)
        pixels[nOut-1] |= 1 << (iIn & 7);
  }
  
  Image2B(BufferedImage img) {
    this(img, 128);
  }
  
  Image2B(BufferedImage img, int threshold) {
    this(new BWImage(img), threshold);
  }
  
  // initializes with black
  Image2B(int w, int h) {
  this.h = h;
  this.w = w;
    pixels = new byte[(w*h+7)/8];
  }
  
  RGBImage toRGB() {
    RGBImage img = new RGBImage(w, h, Color.black);
    for (int y = 0; y < h; y++) for (int x = 0; x < w; x++) {
      int i = y*w+x;
      if ((pixels[i/8] & (1 << (i & 7))) != 0)
        img.setPixel(x, y, Color.white);
    }
    return img;
  }
  
  BWImage toBW() {
    BWImage img = new BWImage(w, h, 0f);
    for (int y = 0; y < h; y++) for (int x = 0; x < w; x++) {
      int i = y*w+x;
      if ((pixels[i/8] & (1 << (i & 7))) != 0)
        img.setPixel(x, y, 1f);
    }
    return img;
  }
  
  public BufferedImage getBufferedImage() { return toBW().getBufferedImage(); }
  
  // x and y must be inside the image
  final public boolean getBoolPixel(int x, int y){ return getPixel(x, y); }
public boolean getPixel(int x, int y) {
    int i = y*w+x;
    return (pixels[i/8] & (1 << (i & 7))) != 0;
  }
  
  // defaultColor is color outside of image
  final public boolean getBoolPixel(int x, int y, boolean defaultColor){ return getPixel(x, y, defaultColor); }
public boolean getPixel(int x, int y, boolean defaultColor) {
    if (x < 0 || y < 0 || x >= w || y >= h) return defaultColor;
    return getPixel(x, y);
  }
  
  public void setPixel(int x, int y, boolean b) {
    int i = y*w+x;
    byte val = pixels[i/8], shifted = (byte) (1 << (i & 7));
    val = (byte) (b ? val | shifted : val & ~shifted);
    pixels[i/8] = val;
  }
  
  void setPixel(int x, int y) {
    int i = y*w+x;
    pixels[i/8] |= 1 << (i & 7);
  }
  
  public int getWidth() { return w; }
  public int getHeight() { return h; }
  
  public String toString() {
    return "Image2B " + str_px(w, h);
  }
  
  // clear unused bits in pixel array after we received
  // a possibly dirty array
  void cleanPixelArray() {
    int n = w*h;
    if ((n & 7) != 0)
      pixels[n/8] &= (1 << (n & 7))-1;
  }
  
  public double averageBrightness() {
    return doubleRatio(bitCount(pixels), w*h);
  }
}
// result image is as large as the region's bounds
// with black pixels inside and white pixels outside the region
static class RegionToImage2B implements IFieldsToList{
  IPixelSet region;
  RegionToImage2B() {}
  RegionToImage2B(IPixelSet region) {
  this.region = region;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + region + ")"; }public Object[] _fieldsToList() { return new Object[] {region}; }

   final public RegionToImage2B setBounds(Rect bounds){ return bounds(bounds); }
public RegionToImage2B bounds(Rect bounds) { this.bounds = bounds; return this; }  final public Rect getBounds(){ return bounds(); }
public Rect bounds() { return bounds; }
 Rect bounds;
  Image2B image;
  
  public void run() { try {
    if (bounds == null) bounds = region.bounds();
    int x1 = bounds.x, y1 = bounds.y, w = bounds.w, h = bounds.h, i = 0;
    byte[] pixels = new byte[(w*h+7)/8];
    for (int y = 0; y < h; y++)
      for (int x = 0; x < w; x++) {
        if (!region.contains(x1+x, y1+y))
          pixels[i/8] |= 1 << (i & 7);
        i++;
      }
      
    image = new Image2B(w, h, pixels);
  } catch (Exception __e) { throw rethrow(__e); } }
  
  Image2B get() {
    if (image == null) run();
    return image;
  }
}
static interface ISetter<A> {
 void set(A a);
}

// The idea is to leave max as the actual number of cores the system
// has (numberOfCores()), and in case of being fully booked, raise an
// alert (customerMustWaitAlert) which can be handled by a strategy
// object (different reactions are possible).
// If nothing is done in such an event, clients are processed serially
// (no guarantees of order), split up among the available threads.

/* SYNChronisation order:
      1. PooledThread
      2. ThreadPool */

static class ThreadPool implements AutoCloseable {
  int max = numberOfCores();
  List<PooledThread> all = new ArrayList();
  Set<PooledThread> used = new HashSet();
  Set<PooledThread> free = new HashSet();
  boolean verbose, retired;
  
  // our own ping surce so we can start threads & keep them running
  class InternalPingSource extends PingSource {}
  InternalPingSource internalPingSource = new InternalPingSource();
  
  MultiSleeper sleeper = new MultiSleeper();
  
  ThreadPool() {}
  ThreadPool(int max) {
  this.max = max;}
  
  synchronized int maxSize() { return max; }
  synchronized int total() { return l(used)+l(free); }
  
   transient Set<Runnable> onCustomerMustWaitAlert;
public  ThreadPool onCustomerMustWaitAlert(Runnable r) { onCustomerMustWaitAlert = createOrAddToSyncLinkedHashSet(onCustomerMustWaitAlert, r); return this; }
public  ThreadPool removeCustomerMustWaitAlertListener(Runnable r) { main.remove(onCustomerMustWaitAlert, r); return this; }
public   void customerMustWaitAlert() {  if (onCustomerMustWaitAlert != null) for (var listener : onCustomerMustWaitAlert) pcallF_typed(listener); }
  
  void fireCustomerMustWaitAlert() {
    vmBus_send("customerMustWaitAlert", this, currentThread());
    customerMustWaitAlert();
  }

  // DOESN'T WAIT. adds action to a thread's queue if nothing is
  // available immediately.
  PooledThread acquireThreadOrQueue(Runnable action) {
    if (action == null) return null;
    PooledThread t;
    synchronized(this) {
      if (_hasFreeAfterCreating()) {
        t = _firstFreeThread();
        markUsed(t);
      } else
        t = _anyThread();
    }
    
    t.addWork(action); // will move it from free to used
    return t;
  }
  
  // run in synchronized block
  boolean _hasFreeAfterCreating() {
    checkNotRetired();
    if (nempty(free)) return true;
    if (total() < max) {
      PooledThread t = newThread();
      all.add(t);
      free.add(t);
      return true;
    }
    return false;
  }
  
  // WAITS until thread is available
  PooledThread acquireThreadOrWait(Runnable action) { try {
    if (action == null) return null;
    PooledThread t;
    while (true) {
      synchronized(this) {
        if (_hasFreeAfterCreating()) {
          t = _firstFreeThread();
          break;
        } else
          _waitWaitWait();
      }
    }
    t.addWork(action);
    return t;
  } catch (Exception __e) { throw rethrow(__e); } }
  
  PooledThread _firstFreeThread() {
    return first(free);
  }
  
  PooledThread _anyThread() {
    return random(used);
  }
  
  class PooledThread extends Thread {
    PooledThread(String name) { super(name); }
    
    AppendableChain<Runnable> q;
    
    synchronized Runnable _grabWorkOrSleep() { try {
      Runnable r = first(q);
      if (r == null) {
        markFree(this);
        if (verbose) print("Thread sleeps");
        synchronized(this) { wait(); }
        if (verbose) print("Thread woke up");
        return null;
      }
      q = popFirst(q);
      return r;
    } catch (Exception __e) { throw rethrow(__e); } }
    
    public void run() { try {
      pingSource_tl().set(internalPingSource);
      while  (!retired()) { ping(); 
        Runnable r = _grabWorkOrSleep();
        if (verbose) print(this + " work: " + r);
        if (r != null)
          try {
            if (verbose) print(this + " running: " + r);
            r.run();
            pingSource_tl().set(internalPingSource);
            if (verbose) print(this + " done");
          } catch (Throwable e) {
            pingSource_tl().set(internalPingSource);
            if (verbose) print(this + " error");
            printStackTrace(e);
          } finally {
            pingSource_tl().set(internalPingSource);          
            if (verbose) print("ThreadPool finally");
          }
      }
    } catch (Exception __e) { throw rethrow(__e); } }
    
    synchronized boolean isEmpty() { return empty(q); }
    
    // append to q (do later)
    void addWork(Runnable r) {
      if (verbose) print("Added work to " + this + ": " + r);
      synchronized(this) {
        q = chainPlus(q, r);
        notifyAll();
      }
    }  
  }
  
  PooledThread newThread() {
    PooledThread t = new PooledThread("Thread Pool Inhabitant " + n2(total()+1));
    t.start();
    return t;
  }
  
  synchronized void markFree(PooledThread t) {
    used.remove(t);
    free.add(t);
    notifyAll();
  }
  
  synchronized void markUsed(PooledThread t) {
    free.remove(t);
    used.add(t);
  }
  
  synchronized public String toString() {
    return retired()
      ? "Retired ThreadPool"
      : "ThreadPool " + roundBracket(commaCombine(
        n2(used) + " used out of " + n2(total()),
        max <= total() ? null : "could grow to " + n2(max)));
  }
  
  synchronized boolean retired() { return retired; }
  synchronized void retire() {
    if (verbose) print("ThreadPool Retiring");
    retired = true;
    for (var thread : free) syncNotifyAll(thread); // wake it up so it exits
  }
  void checkNotRetired() {   
    if (retired()) throw fail("retired");
  }
 
  // We could do a soft-close here (stop the idle threads, let running threads finish, then end those too, stop accepting new orders)
  // or a hard close (interrupt all threads, stop accepting new orders)
  synchronized public void close() { try {
    retire();
  } catch (Exception __e) { throw rethrow(__e); } }
  
  // run in synchronized block
  void _waitWaitWait() { try {
    do {
      fireCustomerMustWaitAlert();
      wait();
      checkNotRetired();
    } while (empty(free));
  } catch (Exception __e) { throw rethrow(__e); } }
  
  void dO(String text, Runnable r) {
    if (r == null) return;
    new PingSource(this, text).dO(r);
  }
  
  ISleeper_v2 sleeper() { return sleeper; }
}
static interface IAutoCloseableF0<A> extends IF0<A>, AutoCloseable {}
/*
 * #!
 * Ontopia Engine
 * #-
 * Copyright (C) 2001 - 2013 The Ontopia Project
 * #-
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 * 
 *      http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 * !#
 */

// modified by Stefan Reich

// Implements the Set interface more compactly than
// java.util.HashSet by using a closed hashtable.

// Note: equals is always called on the _stored_ object, not the one
// passed as an argument to find(), contains() etc.
// (In case you want to put special magic in your equals() function)

static class UnsynchronizedCompactHashSet<A> extends java.util.AbstractSet<A> {
  protected final static int INITIAL_SIZE = 3;
  public final static double LOAD_FACTOR = 0.75;

  protected final static Object nullObject = new Object();
  protected final static Object deletedObject = new Object();
  protected int elements;
  protected int freecells;
  protected A[] objects;
  
  protected int modCount;
  
  
  UnsynchronizedCompactHashSet() {
    this(INITIAL_SIZE);
  }

  UnsynchronizedCompactHashSet(int size) {
    // NOTE: If array size is 0, we get a
    // "java.lang.ArithmeticException: / by zero" in add(Object).
    objects = (A[]) new Object[(size==0 ? 1 : size)];
    elements = 0;
    freecells = objects.length;
    
      modCount = 0;
    
  }

  UnsynchronizedCompactHashSet(Collection<A> c) {
    this(c.size());
    addAll(c);
  }

  @Override
  public Iterator<A> iterator() {
    return new CompactHashIterator<A>();
  }

  @Override
  public int size() {
    return elements;
  }

  @Override
  public boolean isEmpty() {
    return elements == 0;
  }

  @Override
  public boolean contains(Object o) {
    return find(o) != null;
  }
  
  A find(Object o) {
    if (o == null) o = nullObject;
    
    int hash = o.hashCode();
    int index = (hash & 0x7FFFFFFF) % objects.length;
    int offset = 1;

    // search for the object (continue while !null and !this object)
    while(objects[index] != null &&
          !(objects[index].hashCode() == hash &&
            objects[index].equals(o))) {
      index = ((index + offset) & 0x7FFFFFFF) % objects.length;
      offset = offset*2 + 1;

      if (offset == -1)
        offset = 2;
    }

    return objects[index];
  }
  
  boolean removeIfSame(Object o) {
    A value = find(o);
    if (value == o) {
      remove(value);
      return true;
    }
    return false;
  }

  @Override
  public boolean add(Object o) {
    if (o == null) o = nullObject;

    int hash = o.hashCode();
    int index = (hash & 0x7FFFFFFF) % objects.length;
    int offset = 1;
    int deletedix = -1;
    
    // search for the object (continue while !null and !this object)
    while(objects[index] != null &&
          !(objects[index].hashCode() == hash &&
            objects[index].equals(o))) {

      // if there's a deleted object here we can put this object here,
      // provided it's not in here somewhere else already
      if (objects[index] == deletedObject)
        deletedix = index;
      
      index = ((index + offset) & 0x7FFFFFFF) % objects.length;
      offset = offset*2 + 1;

      if (offset == -1)
        offset = 2;
    }
    
    if (objects[index] == null) { // wasn't present already
      if (deletedix != -1) // reusing a deleted cell
        index = deletedix;
      else
        freecells--;

      
        modCount++;
      
      elements++;

      // here we face a problem regarding generics:
      // add(A o) is not possible because of the null Object. We cant do 'new A()' or '(A) new Object()'
      // so adding an empty object is a problem here
      // If (! o instanceof A) : This will cause a class cast exception
      // If (o instanceof A) : This will work fine

      objects[index] = (A) o;
      
      // do we need to rehash?
      if (1 - (freecells / (double) objects.length) > LOAD_FACTOR)
        rehash();
      return true;
    } else // was there already 
      return false;
  }
  
  @Override
  public boolean remove(Object o) {
    if (o == null) o = nullObject;
    
    int hash = o.hashCode();
    int index = (hash & 0x7FFFFFFF) % objects.length;
    int offset = 1;
    
    // search for the object (continue while !null and !this object)
    while(objects[index] != null &&
          !(objects[index].hashCode() == hash &&
            objects[index].equals(o))) {
      index = ((index + offset) & 0x7FFFFFFF) % objects.length;
      offset = offset*2 + 1;

      if (offset == -1)
        offset = 2;
    }

    // we found the right position, now do the removal
    if (objects[index] != null) {
      // we found the object

      // same problem here as with add
      objects[index] = (A) deletedObject;
      
        modCount++;
      
      elements--;
      return true;
    } else
      // we did not find the object
      return false;
  }
  
  @Override
  public void clear() {
    elements = 0;
    for (int ix = 0; ix < objects.length; ix++)
      objects[ix] = null;
    freecells = objects.length;
    
      modCount++;
    
  }

  @Override
  public Object[] toArray() {
    Object[] result = new Object[elements];
    Object[] objects = this.objects;
    int pos = 0;
    for (int i = 0; i < objects.length; i++)
      if (objects[i] != null && objects[i] != deletedObject) {
        if (objects[i] == nullObject)
          result[pos++] = null;
        else
          result[pos++] = objects[i];
      }
    // unchecked because it should only contain A
    return result;
  }

  // not sure if this needs to have generics
  @Override
  public <T> T[] toArray(T[] a) {
    int size = elements;
    if (a.length < size)
      a = (T[])java.lang.reflect.Array.newInstance(
                                 a.getClass().getComponentType(), size);
    A[] objects = this.objects;
    int pos = 0;
    for (int i = 0; i < objects.length; i++)
      if (objects[i] != null && objects[i] != deletedObject) {
        if (objects[i] == nullObject)
          a[pos++] = null;
        else
          a[pos++] = (T) objects[i];
      }
    return a;
  }
  
  protected void rehash() {
    int garbagecells = objects.length - (elements + freecells);
    if (garbagecells / (double) objects.length > 0.05)
      // rehash with same size
      rehash(objects.length);
    else
      // rehash with increased capacity
      rehash(objects.length*2 + 1);
  }
  
  protected void rehash(int newCapacity) {
    int oldCapacity = objects.length;
    @SuppressWarnings("unchecked")
    A[] newObjects = (A[]) new Object[newCapacity];

    for (int ix = 0; ix < oldCapacity; ix++) {
      Object o = objects[ix];
      if (o == null || o == deletedObject)
        continue;
      
      int hash = o.hashCode();
      int index = (hash & 0x7FFFFFFF) % newCapacity;
      int offset = 1;

      // search for the object
      while(newObjects[index] != null) { // no need to test for duplicates
        index = ((index + offset) & 0x7FFFFFFF) % newCapacity;
        offset = offset*2 + 1;

        if (offset == -1)
          offset = 2;
      }

      newObjects[index] = (A) o;
    }

    objects = newObjects;
    freecells = objects.length - elements;
  }
  
  private class CompactHashIterator<T> implements Iterator<T> {
    private int index;
    private int lastReturned = -1;

    
      private int expectedModCount;
    

    @SuppressWarnings("empty-statement")
    public CompactHashIterator() {
        for (index = 0; index < objects.length &&
                        (objects[index] == null ||
                        objects[index] == deletedObject); index++)
          ;
        
          expectedModCount = modCount;
        
    }

    @Override
    public boolean hasNext() {
        return index < objects.length;
    }

    @SuppressWarnings("empty-statement")
    @Override
    public T next() {
        /*if (modCount != expectedModCount)
          throw new ConcurrentModificationException();*/
        int length = objects.length;
        if (index >= length) {
          lastReturned = -2;
          throw new NoSuchElementException();
        }
  
        lastReturned = index;
        for (index += 1; index < length &&
                         (objects[index] == null ||
                          objects[index] == deletedObject); index++)
          ;
        if (objects[lastReturned] == nullObject)
          return null;
        else
          return (T) objects[lastReturned];
    }

    @Override
    public void remove() {
        
          if (modCount != expectedModCount)
            throw new ConcurrentModificationException();
        
        if (lastReturned == -1 || lastReturned == -2)
          throw new IllegalStateException();
        // delete object
        if (objects[lastReturned] != null && objects[lastReturned] != deletedObject) {
          objects[lastReturned] = (A) deletedObject;
          elements--;
          
            modCount++;
            expectedModCount = modCount; // this is expected; we made the change
          
        }
    }
  }
  
  int capacity() { return objects.length; }
  
  // returns true if there was a shrink
  boolean shrinkToFactor(double factor) {
    if (factor > LOAD_FACTOR)
      throw fail("Shrink factor must be equal to or smaller than load factor: " + factor + " / " + LOAD_FACTOR);
    int newCapacity = max(INITIAL_SIZE, iround(size()/factor));
    if (newCapacity >= capacity()) return false;
    rehash(newCapacity);
    return true;
  }
}
abstract static class IntegerIterator {
  abstract boolean hasNext();
  abstract int next();
}
static interface MakesBufferedImage extends WidthAndHeight {
  BufferedImage getBufferedImage();
  
  public default void drawAt(Graphics2D g, int x, int y) {
    g.drawImage(getBufferedImage(), x, y, null);
  }
  
  
    default int getWidth() { return getBufferedImage().getWidth(); }
  

    default int getHeight() { return getBufferedImage().getHeight(); }
  

}
static final class BWImage extends Meta implements MakesBufferedImage, IBWImage {
  int width, height;
  byte[] pixels;

  // color returned when getPixel is called with a position outside the actual image
  float borderColor = 0.0f;
  
  // for unstructure()
  BWImage() {}

  // BLACK!
  BWImage(int width, int height) {
  this.height = height;
  this.width = width;
    pixels = new byte[width*height];
  }

  BWImage(int width, int height, float brightness) {
  this.height = height;
  this.width = width;
    pixels = new byte[width*height];
    fillArrayUnlessZero(pixels, _toByte(brightness));
  }
  
  BWImage(int width, int height, float[] pixels) {
    this.pixels = new byte[pixels.length];
  this.height = height;
  this.width = width;
    for (int i = 0; i < pixels.length; i++)
      this.pixels[i] = _toByte(pixels[i]);
  }

  public BWImage(int width, int height, byte[] pixels) {
    this.height = height;
    this.width = width;
    this.pixels = pixels;
  }

  public BWImage(BWImage image) {
    width = image.getWidth();
    height = image.getHeight();
    byte[] pixels = this.pixels = new byte[width*height];
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++)
        pixels[y*width+x] = image.getByte(x, y);
  }

  // TODO: optimize!
  BWImage(RGBImage image) {
    width = image.getWidth();
    height = image.getHeight();
    byte[] pixels = this.pixels = new byte[height*width];
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++) {
        RGB rgb = image.getRGB(x, y);
        pixels[y*width+x] = BWImage._toByte(rgb.getBrightness());
      }
  }

  /*public BWImage(BufferedImage image) {
    this(new RGBImage(image));
  }*/

  BWImage(BufferedImage image) { try {
    width = image.getWidth();
    height = image.getHeight();
    int[] pixels = new int[width*height];
    byte[] bytePixels = this.pixels = new byte[width*height];
    PixelGrabber pixelGrabber = new PixelGrabber(image, 0, 0, width, height, pixels, 0, width);
    if (!pixelGrabber.grabPixels())
      throw fail("Could not grab pixels");
    int n = width*height;
    
    for (int i = 0; i < n; i++) {
      //bytePixels[i] = pixelToByte(pixels[i]);
      int packed = pixels[i];
      /*float r = ((packed >> 16) & 0xFF)/255f;
      float g = ((packed >> 8) & 0xFF)/255f;
      float b = (packed & 0xFF)/255f;
      bytePixels[i] = (byte) iround((r+g+b)/3.0f*255f);*/
      int r = ((packed >> 16) & 0xFF);
      int g = ((packed >> 8) & 0xFF);
      int b = (packed & 0xFF);
      bytePixels[i] = (byte) ((r+g+b+1)/3);
    }
  } catch (Exception __e) { throw rethrow(__e); } }
  
  // TODO: does it exactly match the other method? (asRGB+getBrightness+_toByte)
  static byte pixelToByte(int packed) {
    /*int r = (packed >> 16) & 0xFF;
    int g = (packed >> 8) & 0xFF;
    int b = packed & 0xFF;
    ret (byte) ((r+g+b)/3.0f);*/
    float r = ((packed >> 16) & 0xFF)/255f;
    float g = ((packed >> 8) & 0xFF)/255f;
    float b = (packed & 0xFF)/255f;
    return (byte) ((r+g+b)/3.0f*255f);
  }

  public byte getByte(int x, int y) {
    return inRange(x, y) ? getByte_noRangeCheck(x, y) : _toByte(borderColor);
  }
  
  // pretty bad function name
  // gets brightness (0 to 255) at pixel
  public int getInt(int x, int y) {
    return ubyteToInt(getByte(x, y));
  }
  
  // idx = index in pixel array
  public int getInt_noRangeCheck(int idx) {
    return ubyteToInt(pixels[idx]);
  }
  
  // gets brightness (0 to 255) at pixel with default if out of image
  public int getInt(int x, int y, int defaultValue) {
    return inRange(x, y) ? getInt(x, y) : defaultValue;
  }
  
  public double averageBrightness() {
    double sum = 0;
    int n = width*height;
    for (int i = 0; i < n; i++)
      sum += getInt_noRangeCheck(i);
    return sum/n;
  }

  public float minimumBrightness() {
    float min = 1;
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++)
        min = Math.min(min, getPixel(x, y));
    return min;
  }

  public float maximumBrightness() {
    float max = 0;
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++)
        max = Math.max(max, getPixel(x, y));
    return max;
  }

  float getPixel(int x, int y) {
    return inRange(x, y) ? _toFloat(getByte(x,y )) : borderColor;
  }
  
  public float getFloatPixel(int x, int y) { return getPixel(x, y); }
  
  float getPixel(Pt p) { return getPixel(p.x, p.y); }

  static byte _toByte(float pixel) {
    return (byte) (pixel*255f);
  }

  static float _toFloat(byte pixel) {
    return (((int) pixel) & 255)/255f;
  }

  private boolean inRange(int x, int y) {
    return x >= 0 && x < width && y >= 0 && y < height;
  }

  public int getWidth() { return width; }
  public int getHeight() { return height; }

  public RGBImage toRGB() {
    int[] rgbs = new int[width*height];
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++) {
        int b = getByte(x, y) & 0xFF;
        rgbs[y*width+x] = 0xFF000000 | b*0x010101;
      }
    return new RGBImage(width, height, rgbs);
  }
  
  public RGBImage toRGB_slow() {
    RGB[] rgbs = new RGB[width*height];
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++) {
        float p = getPixel(x, y);
        rgbs[y*width+x] = new RGB(p, p, p);
      }
    return new RGBImage(width, height, rgbs);
  }


  public BWImage clip(int x, int y, int w, int h) {
    return clip(new Rectangle(x, y, w, h));
  }

  private Rectangle fixClipRect(Rectangle r) {
    return r.intersection(new Rectangle(0, 0, width, height));
  }

  BWImage clip(Rect r) {
    return clip(r.getRectangle());
  }
  
  /** this should be multithread-safe */
  public BWImage clip(Rectangle r) {
    r = fixClipRect(r);
    byte[] newPixels = new byte[r.height*r.width];
    for (int y = 0; y < r.height; y++)
      for (int x = 0; x < r.width; x++)
        newPixels[y*r.width+x] = getByte(r.x+x, r.y+y);
    return new BWImage(r.width, r.height, newPixels);
  }

  public void setPixel(int x, int y, float brightness) {
    setByte(x, y, _toByte(fixPixel(brightness)));
  }
  
  // i = 0 to 255
  public void setInt(int x, int y, int i) {
    setByte(x, y, (byte) limitToUByte(i));
  }
  
  public void setInt(Pt p, int i) {
    setInt(p.x, p.y, i);
  }
  
  public void setByte(int x, int y, byte b) {
    if (x >= 0 && x < width && y >= 0 && y < height)
      pixels[y*width+x] = b;
  }

  byte getByte_noRangeCheck(int x, int y) {
    return pixels[y*width+x];
  }

  public void setByte(int x, int y, int brightness) {
    setByte(x, y, (byte) brightness);
  }

  private float fixPixel(float pixel) {
    return Math.max(0, Math.min(1, pixel));
  }

  public float getBorderColor() {
    return borderColor;
  }

  public void setBorderColor(float borderColor) {
    this.borderColor = borderColor;
  }

  public boolean anyPixelBrighterThan(double threshold) {
    for (int y = 0; y < height; y++)
      for (int x = 0; x < width; x++)
        if (getPixel(x, y) > threshold)
          return true;
    return false;
  }
  
  int[] getRGBPixels() {
    int n = width*height;
    int[] out = new int[n];
    for (int i = 0; i < n; i++) {
      var b = ubyteToInt(pixels[i]);
      b |= (b << 8) | (b << 16);
      out[i] = b | 0xFF000000;
    }
    return out;
  }
  
  public BufferedImage getBufferedImage() {
    return bufferedImage(getRGBPixels(), width, height);
  }
  
  byte[] getBytes() {
    return pixels;
  }
}
interface IPixelSet extends HasBounds {
  public boolean contains(int x, int y);
  
  default boolean contains(Pt p) { return contains(p.x, p.y); }
  
  default public IterableIterator<Pt> pixelIterator() {
    return filterI(main.pixelIterator(bounds()), p -> contains(p));
  }
}
interface INumberOfPixels {
  int numberOfPixels();
}
interface Matrix<A> extends WidthAndHeight {
  public A get(int x, int y);
  public void set(int x, int y, A a);
  
  default Pt size() { return pt(getWidth(), getHeight()); }
  default int nCells() { return getWidth()*getHeight(); }
  
  default A get(Pt p) { return get(p.x, p.y); }
  default void put(Pt p, A a){ set(p, a); }
default void set(Pt p, A a) { set(p.x, p.y, a); }
  
  // one row of the matrix as a virtual list (mutable)
  default List<A> getLine(int y) {
    return new RandomAccessAbstractList<A>() {
      public int size() { return getWidth(); }
      
      public A get(int x) {
        return Matrix.this.get(x, y);
      }
      
      public A set(int x, A val) {
        A old = Matrix.this.get(x, y);
        Matrix.this.set(x, y, val);
        return old;
      }
    };
  }
}
static class OnePathWithOrigin extends OnePath {
   final public OnePathWithOrigin setOrigin(Pt origin){ return origin(origin); }
public OnePathWithOrigin origin(Pt origin) { this.origin = origin; return this; }  final public Pt getOrigin(){ return origin(); }
public Pt origin() { return origin; }
 Pt origin = pt(0, 0);
  
  OnePathWithOrigin() {}
  OnePathWithOrigin(String path) { super(path); }
  OnePathWithOrigin(Pt origin, String path) { super(path);
  this.origin = origin; }
  OnePathWithOrigin(int originX, int originY, String path) { super(path); origin = pt(originX, originY); }
  OnePathWithOrigin(Iterable<Pt> points, boolean close) {
    var l = asList(points);
    origin = first(l);
    fromPoints(l, close);
  }
  
  OnePathWithOrigin(OnePathWithOrigin path) {
    super(path);
    origin = path.origin;
  }
  
  public String toString() {
    return "Origin (" + origin + "), path: " + super.toString();
  }
  
  OnePathWithOrigin reversed() {
    return new OnePathWithOrigin(reversedList(pointList()), false);
  }
}
interface ISleeper_v2 {
  default Sleeping doLater(long targetTime, Runnable r) {
    return doLater(sysTimeToTimestamp(targetTime), r);
  }
  
  Sleeping doLater(Timestamp targetTime, Runnable r);
  
  public default Sleeping doAfter(double seconds, Runnable r) {
    return doLater(tsNow().plusSeconds(seconds), r);
  }
}
interface IMultiMap<A, B> {
  public Set<A> keySet();
  public Collection<B> get(A a);
  public int size();
  public int keyCount();
}
interface IDoublePt {
  public double x_double();
  public double y_double();
}
static interface IVar<A> extends IF0<A> {
  void set(A a);
  A get();
  
  // reified type of value (if available)
  default Class<A> getType() { return null; }
  
  default IF0<A> getter() { return () -> get(); }
  default IVF1<A> setter() { return __1 -> set(__1); }
  
  
  default boolean has() { return get() != null; }
  default void clear() { set(null); }
  
}


abstract static class Sleeping implements AutoCloseable , IFieldsToList{
  Timestamp targetTime;
  Runnable action;
  Sleeping() {}
  Sleeping(Timestamp targetTime, Runnable action) {
  this.action = action;
  this.targetTime = targetTime;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + targetTime + ", " + action + ")"; }public Object[] _fieldsToList() { return new Object[] {targetTime, action}; }

  long remainingMS() { return targetTime.minus(tsNow()); }
}
// AppendableChain has one "smart" head element (with size counter
// and pointer to the chain's last element), all the other nodes are
// maximally simple (MinimalChain).
// This allows O(1) front insertion, front removal and back insertion
// (not removal at the back though) which is fine for what I need this
// for (event queues).
//
// Stefan Reich, Oct 21

static class AppendableChain<A> extends MinimalChain<A> implements Iterable<A>, IntSize {
  MinimalChain<A> last; // pointer to last element in chain (which may be us)
   final public int getSize(){ return size(); }
public int size() { return size; }
 int size; // total length of chain

  AppendableChain() {} // only used internally
  AppendableChain(A element) {
  this.element = element; size = 1; last = this; }
  
  // intermediate constructor called by itemPlusChain()
  AppendableChain(A element, AppendableChain<A> next) {
  this.next = next;
  this.element = element;
    if (next == null) return;
    
    MinimalChain<A> b = new MinimalChain();
    b.element = next.element;
    b.next = next.next;
    this.next = b;
    last = next.last;
    size = next.size+1;
  }
  
  public String toString() { return str(toList()); }
  
  // append at the end
  boolean add(A a) {
    MinimalChain newLast = new MinimalChain(a);
    last.next = newLast;
    last = newLast;
    ++size;
    return true;
  }
  
  // drop first element
  AppendableChain<A> popFirst() {
    if (next == null) return null;
    element = next.element;
    if (last == next) last = this;
    next = next.next;
    --size;
    return this;
  }
  
  ArrayList<A> toList() {
    ArrayList<A> l = emptyList(size);
    MinimalChain<A> c = this;
    while (c != null) {
      l.add(c.element);
      c = c.next;
    }
    return l;
  }
  
  //public Iterator<A> iterator() { ret toList().iterator(); }
  
  class ACIt extends IterableIterator  < A > {
    MinimalChain<A> c = AppendableChain.this;
    
    public boolean hasNext() {
      return c != null;
    }
    
    public A next() {
      var a = c.element;
      c = c.next;
      return a;
    }
  }
  
  public IterableIterator<A> iterator() {
    return new ACIt();
  }
}
static class MultiSleeper extends RestartableCountdown implements ISleeper_v2 {
  MultiSetMap<Timestamp, Runnable> entries = treeMultiSetMap();
  
  void check() {
    var time = nextWakeUpTime();
    var action = firstValue(entries);
    setTargetTime(time == null ? 0 : time.sysTime(), new Runnable() {  public void run() { try { 
      Set<Runnable> toCall;
      synchronized(MultiSleeper.this) {
        toCall = entries.get(time);
        entries.remove(time);
        check();
      }
      pcallFAll(toCall);
    
} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "Set<Runnable> toCall;\r\n      synchronized(MultiSleeper.this) {\r\n        toCal..."; }});
  }
  
  synchronized void removeEntry(Timestamp targetTime, Runnable action) {
    entries.remove(targetTime, action);
  }
  
  // API
  
  synchronized Timestamp nextWakeUpTime() {
    return firstKey(entries);
  }
  
  public synchronized Sleeping doLater(Timestamp targetTime, Runnable r) {
    if (r == null || targetTime == null) return null;
    targetTime = max(targetTime, tsNow());
    entries.put(targetTime, r);
    check();
    return new Sleeping(targetTime, r) {
      public void close() { try {
        removeEntry(targetTime, r);
      } catch (Exception __e) { throw rethrow(__e); } }
    };
  }
}
static class RGBImage implements MakesBufferedImage, IRGBImage {
  transient BufferedImage bufferedImage;
  int width, height;
  int[] pixels;

  RGBImage() {}

  RGBImage(BufferedImage image) {
    bufferedImage = image;
    width = image.getWidth();
    height = image.getHeight();
    pixels = new int[width*height];
    var gp = grabbableIntPixels_fastOrSlow(image);
    
    if (gp.scanlineStride == width && gp.offset == 0)
      pixels = gp.data;
    else {
      pixels = new int[width*height];
      int iIn = 0, iOut = 0;
      for (int y = 0; y < height; y++) {
        arrayCopy(gp.data, iIn, pixels, iOut, width);
        iIn += gp.scanlineStride;
        iOut += width;
      }
    }
    
    cleanPixels(); // set upper byte to 0
  }

  RGBImage(Dimension size, Color color) {
    this(size.width, size.height, color);
  }

  RGBImage(Dimension size, RGB color) {
    this(size.width, size.height, color);
  }

  private void cleanPixels() {
    var pixels = this.pixels;
    for (int i = 0; i < pixels.length; i++)
      pixels[i] &= 0xFFFFFF;
  }

  RGBImage(int width, int height, int[] pixels) {
    this.width = width;
    this.height = height;
    this.pixels = pixels;
  }

  RGBImage(int w, int h, RGB[] pixels) {
    this.width = w;
    this.height = h;
    this.pixels = asInts(pixels);
  }

  public static int[] asInts(RGB[] pixels) {
    int[] ints = new int[pixels.length];
    for (int i = 0; i < pixels.length; i++)
      ints[i] = pixels[i] == null ? 0 : pixels[i].getColor().getRGB();
    return ints;
  }

  public RGBImage(int w, int h) {
    this(w, h, Color.black);
  }
  
  RGBImage(int w, int h, RGB rgb) {
    this.width = w;
    this.height = h;
    this.pixels = new int[w*h];
    int col = rgb.asInt();
    if (col != 0)
      for (int i = 0; i < pixels.length; i++)
        pixels[i] = col;
  }

  RGBImage(RGBImage image) {
    this(image.width, image.height, copyPixels(image.pixels));
  }

  RGBImage(int width, int height, Color color) {
    this(width, height, new RGB(color));
  }

  RGBImage(MakesBufferedImage img) {
    this(toBufferedImage(img));
  }

  private static int[] copyPixels(int[] pixels) {
    int[] copy = new int[pixels.length];
    System.arraycopy(pixels, 0, copy, 0, pixels.length);
    return copy;
  }

  public int getIntPixel(int x, int y) {
    if (inRange(x, y))
      return pixels[y * width + x];
    else
      return 0xFFFFFF;
  }
  
  // idx = index in pixel array
  public int getIntPixel_noRangeCheck(int idx) {
    return pixels[idx];
  }

  public static RGB asRGB(int packed) {
    int r = (packed >> 16) & 0xFF;
    int g = (packed >> 8) & 0xFF;
    int b = packed & 0xFF;
    return new RGB(r / 255f, g / 255f, b / 255f);
  }

  public RGB getRGB(int x, int y) {
    if (inRange(x, y))
      return asRGB(pixels[y * width + x]);
    else
      return new RGB(0xFFFFFF);
  }

  /** alias of getRGB - I kept typing getPixel instead of getRGB all the time, so I finally created it */
  RGB getPixel(int x, int y) {
    return getRGB(x, y);
  }
  
  RGB getPixel(Pt p) { return getPixel(p.x, p.y); }

  public int getWidth() { return width; }
  public int getHeight() { return height; }
  public int w() { return width; }
  public int h() { return height; }

  /** Attention: cached, i.e. does not change when image itself changes */
  /** @NotNull */
  public BufferedImage getBufferedImage() {
    if (bufferedImage == null) {
      bufferedImage = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB);
      //bufferedImage.setData(Raster.createRaster(new SampleModel()));
      for (int y = 0; y < height; y++)
        for (int x = 0; x < width; x++)
          bufferedImage.setRGB(x, y, pixels[y*width+x]);
    }
    return bufferedImage;
  }

  RGBImage clip(Rect r) {
    return r == null ? null : clip(r.getRectangle());
  }
  
  RGBImage clip(Rectangle r) {
    r = fixClipRect(r);
    if (r.x == 0 && r.y == 0 && r.width == width && r.height == height) return this;
    int[] newPixels;
    try {
      newPixels = new int[r.width*r.height];
    } catch (RuntimeException e) {
      System.out.println(r);
      throw e;
    }
    for (int y = 0; y < r.height; y++) {
      System.arraycopy(pixels, (y+r.y)*width+r.x, newPixels, y*r.width, r.width);
    }
    return new RGBImage(r.width, r.height, newPixels);
  }

  private Rectangle fixClipRect(Rectangle r) {
    r = r.intersection(new Rectangle(0, 0, width, height));
    if (r.isEmpty())
      r = new Rectangle(r.x, r.y, 0, 0);
    return r;
  }

  public int getInt(int x, int y) {
    return pixels[y * width + x];
  }

  public void save(File file) {
    saveImage(file, getBufferedImage());
  }

  public static RGBImage dummyImage() {
    return new RGBImage(1, 1, new int[] {0xFFFFFF});
  }

  public int[] getPixels() {
    return pixels;
  }
  
  void setPixel(int x, int y, int r, int g, int b) {
    if (x >= 0 && y >= 0 && x < width && y < height)
      pixels[y*width+x] = (limitToUByte(r) << 16) | (limitToUByte(g) << 8) | limitToUByte(b);
  }

  public void setPixel(int x, int y, RGB rgb) {
    if (x >= 0 && y >= 0 && x < width && y < height)
      pixels[y*width+x] = rgb.asInt();
  }

  final public void set(int x, int y, Color color){ setPixel(x, y, color); }
public void setPixel(int x, int y, Color color) {
    setPixel(x, y, new RGB(color));
  }
  
  void setInt(int x, int y, int rgb) {
    setPixel(x, y, rgb);
  }

  public void setPixel(int x, int y, int rgb) {
    if (x >= 0 && y >= 0 && x < width && y < height)
      pixels[y*width+x] = rgb;
  }
  
  void setPixel(Pt p, RGB rgb) { setPixel(p.x, p.y, rgb); }
  void setPixel(Pt p, Color color) { setPixel(p.x, p.y, color); }

  public RGBImage copy() {
    return new RGBImage(this);
  }

  public boolean inRange(int x, int y) {
    return x >= 0 && y >= 0 && x < width && y < height;
  }

  public Dimension getSize() {
    return new Dimension(width, height);
  }

  @Override
  public boolean equals(Object o) {
    if (this == o) return true;
    if (o == null || getClass() != o.getClass()) return false;

    RGBImage rgbImage = (RGBImage) o;

    if (height != rgbImage.height) return false;
    if (width != rgbImage.width) return false;
    if (!Arrays.equals(pixels, rgbImage.pixels)) return false;

    return true;
  }

  @Override
  public int hashCode() {
    int result = width;
    result = 31 * result + height;
    result = 31 * result + Arrays.hashCode(pixels);
    return result;
  }

  public String getHex(int x, int y) {
    return getPixel(x, y).getHexString();
  }

  public RGBImage clip(int x, int y, int width, int height) {
    return clip(new Rectangle(x, y, width, height));
  }

  public RGBImage clipLine(int y) {
    return clip(0, y, width, 1);
  }

  public int numPixels() {
    return width*height;
  }
  
  RGBImage uncacheBufferedImage() {
    bufferedImage = null;
    return this;
  }
}

static class Timestamp implements Comparable<Timestamp> , IFieldsToList{
  long date;
  Timestamp(long date) {
  this.date = date;}

public boolean equals(Object o) {
if (!(o instanceof Timestamp)) return false;
    Timestamp __1 =  (Timestamp) o;
    return date == __1.date;
}

  public int hashCode() {
    int h = 2059094262;
    h = boostHashCombine(h, _hashCode(date));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {date}; }

  Timestamp() { date = now(); }
  Timestamp(Date date) { if (date != null) this.date = date.getTime(); }
  
  final long toLong(){ return unixDate(); }
long unixDate() { return date; }
  long unixSeconds() { return unixDate()/1000; }
  
  public String toString() { return formatLocalDateWithSeconds(date); }
  
  // Hmm. Should Timestamp(0) be equal to null? Question, questions...
  public int compareTo(Timestamp t) {
    return t == null ? 1 : cmp(date, t.date);
  }
  
  Timestamp plus(Seconds seconds) {
    return plus(seconds == null ? null : seconds.getDouble());
  }
  
  final Timestamp plusSeconds(double seconds){ return plus(seconds); }
Timestamp plus(double seconds) {
    return new Timestamp(date+toMS(seconds));
  }
  
  // returns milliseconds
  long minus(Timestamp ts) {
    return unixDate()-ts.unixDate();
  }
  
  long sysTime() {
    return clockTimeToSystemTime(date);
  }
  
  Duration minusAsDuration(Timestamp ts) {
    return Duration.ofMillis(minus(ts));
  }
}
static class OnePath {
  ByteBuffer steps = new ByteBuffer();
  
  OnePath() {}
  OnePath(String path) {
    int n = l(path);
    steps.allocate(n);
    for (int i = 0; i < n; i++)
      steps.add(parseDigit(path, i));
  }
  
  OnePath(OnePath path) {
    steps = new ByteBuffer(path.steps);
  }

  // uses first point as origin, so there will be l(points)-1 steps.
  // Unless you set close to true, then it adds the first point at the end again.
  
  OnePath(Iterable<Pt> points, boolean close) {
    fromPoints(points, close);
  }
  
  void fromPoints(Iterable<Pt> points, boolean close) {
    var it = iterator(points);
    if (empty(it)) return;
    Pt firstPoint = it.next(), p = firstPoint;
    while (it.hasNext()) {
      Pt p2 = it.next();
      steps.add(ptToDigit(ptMinus(p2, p)));
      p = p2;
    }
    
    if (close)
      steps.add(ptToDigit(ptMinus(firstPoint, p)));
  }
  
  final int length(){ return size(); }
final int nSteps(){ return size(); }
int size() { return steps.size(); }
  
  public String toString() { return pathString(); }
  
  String pathString() {
    return singleDigitBytesToString(steps);
  }
  
  // includes first point, so returns length()+1 points in total
  IterableIterator<Pt> pointIterator() { return pointIterator(origin()); }
IterableIterator<Pt> pointIterator(Pt startPt) {
    return new IterableIterator<Pt>() {
      int i = 0, n = length();
      Pt p = startPt;
      
      public boolean hasNext() { return i <= n; }
      
      public Pt next() {
        var p = this.p;
        if (i < n) this.p = translatePt(this.p, getStepAsPt(i));
        ++i;
        return p;
      }
    };
  }
  
  final List<Pt> pointsList(){ return pointList(); }
List<Pt> pointList() { return ptBuffer(pointIterator()); }
  
  int getStep(int i) { return steps.get(i); }
  
  Pt getStepAsPt(int i) {
    return onePathDirections()[steps.get(i)];
  }
  
  static int ptToDigit(Pt p) {
    return p.y < 0 ? p.x < 0 ? 1 : p.x == 0 ? 2 : 3
      : p.y == 0 ? p.x < 0 ? 8 : p.x == 0 ? 0 : 4
      : p.x < 0 ? 7 : p.x == 0 ? 6 : 5;
  }
  
  Pt origin() { return main.origin(); }
  Pt endPoint() { return last(pointIterator()); }
  
  Pt drift() {
    return ptMinus(endPoint(), origin());
  }
  
  void addStep(int p_x, int p_y) { addStep(pt(p_x, p_y)); }

void addStep(Pt p) {
    int step = onePathLookupDirection(p);
    if (step < 0) throw fail("Invalid one path step: " + p);
    addStep(step);
  }
  
  void addStep(int step) {
    assertBetween(0, 8, step);
    steps.add(step);
  }
  
  void insertStep(int idx, int p_x, int p_y) { insertStep(idx, pt(p_x, p_y)); }

void insertStep(int idx, Pt p) {
    int step = onePathLookupDirection(p);
    if (step < 0) throw fail("Invalid one path step: " + p);
    insertStep(idx, step);
  }
  
  void insertStep(int idx, int step) {
    assertBetween(0, 8, step);
    steps.add(idx, step);
  }
  
  Rect bounds() {
    return boundsOfPts(pointIterator());
  }
}
static interface IBinaryImage extends MakesBufferedImage {
  boolean getBoolPixel(int x, int y);
  
  default void setPixel(int x, int y, boolean b) { throw unimplemented(); }
  
  default boolean getBoolPixel(Pt p) {
    return getBoolPixel(p.x, p.y);
  }
  
  default boolean getBoolPixel_noRangeCheck(int x, int y) { return getBoolPixel(x, y); }

  public default BufferedImage getBufferedImage() {
    return toImage2B().getBufferedImage();
  }
  
  default Image2B toImage2B() {
    return this instanceof Image2B ? (Image2B) this : iBinaryImageToImage2B(this);
  }
}
interface HasBounds extends WidthAndHeight {
  Rect bounds();
  
  default int getWidth() { return bounds().h; }
  default int getHeight() { return bounds().w; }
}


// uses hash sets as inner sets unless subclassed
// uses a hash map as the outer map by default
static class MultiSetMap<A, B>implements IMultiMap<A, B> {
  Map<A, Set<B>> data = new HashMap<A, Set<B>>();
  int size; // number of values
  
  MultiSetMap() {}
  MultiSetMap(boolean useTreeMap) { if (useTreeMap) data = new TreeMap(); }
  MultiSetMap(MultiSetMap<A, B> map) { putAll(map); }
  MultiSetMap(Map<A, Set<B>> data) {
  this.data = data;}

  boolean put(A key, B value) { synchronized(data) {
    Set<B> set = data.get(key);
    if (set == null)
      data.put(key, set = _makeEmptySet());
    if (!set.add(value)) return false;
    { ++size; return true; }
  }}

  boolean add(A key, B value) { return put(key, value); }

  void addAll(A key, Collection<B> values) { synchronized(data) {
    putAll(key, values);
  }}
  
  void addAllIfNotThere(A key, Collection<B> values) { synchronized(data) {
    for (B value : values)
      setPut(key, value);
  }}
  
  void setPut(A key, B value) { synchronized(data) {
    if (!containsPair(key, value))
      put(key, value);
  }}
  
  final boolean contains(A key, B value){ return containsPair(key, value); }
boolean containsPair(A key, B value) { synchronized(data) {
    return get(key).contains(value);
  }}
  
  void putAll(A key, Collection<B> values) { synchronized(data) {
    for (B value : values)
      put(key, value);
  }}

  void removeAll(A key, Collection<B> values) { synchronized(data) {
    for (B value : values)
      remove(key, value);
  }}
  
  public Set<B> get(A key) { synchronized(data) {
    Set<B> set = data.get(key);
    return set == null ? Collections.<B> emptySet() : set;
  }}
  
  List<B> getAndClear(A key) { synchronized(data) {
    List<B> l = cloneList(data.get(key));
    remove(key);
    return l;
  }}

  // return null if empty
  Set<B> getOpt(A key) { synchronized(data) {
    return data.get(key);
  }}

  // returns actual mutable live set
  // creates the set if not there
  Set<B> getActual(A key) { synchronized(data) {
    Set<B> set = data.get(key);
    if (set == null)
      data.put(key, set = _makeEmptySet());
    return set;
  }}
 
  // TODO: this looks unnecessary
  void clean(A key) { synchronized(data) {
    Set<B> list = data.get(key);
    if (list != null && list.isEmpty())
      data.remove(key);
  }}

  final public Set<A> keys(){ return keySet(); }
public Set<A> keySet() { synchronized(data) {
    return data.keySet();
  }}

  void remove(A key) { synchronized(data) {
    size -= l(data.get(key));
    data.remove(key);
  }}

  void remove(A key, B value) { synchronized(data) {
    Set<B> set = data.get(key);
    if (set != null) {
      if (set.remove(value)) {
        --size;
        if (set.isEmpty())
          data.remove(key);
      }
    }
  }}

  void clear() { synchronized(data) {
    data.clear();
    size = 0;
  }}

  boolean containsKey(A key) { synchronized(data) {
    return data.containsKey(key);
  }}

  B getFirst(A key) { synchronized(data) {
    return first(get(key));
  }}
  
  void addAll(MultiSetMap<A, B> map) { putAll(map); }
  
  void putAll(MultiSetMap<A, B> map) { synchronized(data) {
    for (A key : map.keySet())
      putAll(key, map.get(key));
  }}
  
  void putAll(Map<A, B> map) { synchronized(data) {
    if (map != null) for (Map.Entry<A, B> e : map.entrySet())
      put(e.getKey(), e.getValue());
  }}
  
  final public int keyCount(){ return keysSize(); }
public int keysSize() { synchronized(data) { return l(data); }}
  
  // full size
  public int size() { synchronized(data) {
    return size;
  }}
  
  // count values for key
  int getSize(A key) { return l(data.get(key)); }
  int count(A key) { return getSize(key); }
  
  // expensive operation
  Set<A> reverseGet(B b) { synchronized(data) {
    Set<A> l = new HashSet();
    for (A key : data.keySet())
      if (data.get(key).contains(b))
        l.add(key);
    return l;
  }}
  
  // expensive operation
  A keyForValue(B b) { synchronized(data) {
    for (A key : data.keySet())
      if (data.get(key).contains(b))
        return key;
    return null;
  }}
  
  Map<A, Set<B>> asMap() { synchronized(data) {
    return cloneMap(data);
  }}
  
  boolean isEmpty() { synchronized(data) { return data.isEmpty(); }}
  
  // override in subclasses
  Set<B> _makeEmptySet() {
    return new HashSet();
  }
  
  Collection<Set<B>> allLists() {
    synchronized(data) {
      return new HashSet(data.values());
    }
  }
  
  List<B> allValues() {
    return concatLists(values(data));
  }
  
  List<Pair<A, B>> allEntries() { synchronized(data) {
    List<Pair<A, B>> l = emptyList(size);
    for (Map.Entry<? extends A, ? extends Set<B>> __0 : _entrySet( data))
      { A a = __0.getKey(); Set<B> set = __0.getValue();  for (B b : set)
        l.add(pair(a, b)); }
    return l;
  }}
  
  Object mutex() { return data; }
  
  public String toString() { return "mm" + str(data); }
  
  Pair<A, B> firstEntry() { synchronized(data) {
    if (empty(data)) return null;
    Map.Entry<A, Set<B>> entry = data.entrySet().iterator().next();
    return pair(entry.getKey(), first(entry.getValue()));
  }}
  
  A firstKey() { synchronized(data) { return main.firstKey(data); }}
  A lastKey() { synchronized(data) { return (A) ((NavigableMap) data).lastKey(); }}
  
  A higherKey(Object a) { synchronized(data) { return (A) ((NavigableMap) data).higherKey(a); }}
}
static class MinimalChain<A> implements Iterable<A> {
  A element;
  MinimalChain<A> next;

  MinimalChain() {}
  MinimalChain(A element) {
  this.element = element;}
  MinimalChain(A element, MinimalChain<A> next) {
  this.next = next;
  this.element = element;}
  
  public String toString() { return str(toList()); }
  
  ArrayList<A> toList() {
    ArrayList<A> l = new ArrayList();
    MinimalChain<A> c = this;
    while (c != null) {
      l.add(c.element);
      c = c.next;
    }
    return l;
  }
  
  void setElement(A a) { element = a; }
  void setNext(MinimalChain<A> next) { this.next = next; }
  
  // TODO: optimize
  public Iterator<A> iterator() { return toList().iterator(); }
  
  A get() { return element; }
}
static class RestartableCountdown implements AutoCloseable {
  java.util.Timer timer;
  long targetTime; // in sys time

  
  long /*firings,*/ totalSleepTime; // stats
  
  
  synchronized void setTargetTime(long targetTime, Runnable action) {
    if (targetTime <= 0)
      stop();
    else if (targetTime != this.targetTime) {
      start(targetTime-sysNow(), action);
      this.targetTime = targetTime;
    }
  }
  
  // stops the countdown and restarts it
  synchronized void start(long delayMS, Object action) {
    stop();
    if (delayMS <= 0)
      { startThread(new Runnable() {  public void run() { try {  callF(action); 
} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "callF(action);"; }}); }
    else {
      
        totalSleepTime += delayMS;
      
      timer = doLater_daemon(delayMS, action);
      targetTime = sysNow()+delayMS;
    }
  }
  
  void start(double delaySeconds, Object action) {
    start(toMS(delaySeconds), action);
  }
  
  synchronized void stop() {
    cancelTimer(timer);
    timer = null;
    targetTime = 0;
  }
  
  public void close() { stop(); }
}
static class Seconds implements Comparable<Seconds> , IFieldsToList{
  double seconds;
  Seconds() {}
  Seconds(double seconds) {
  this.seconds = seconds;}

public boolean equals(Object o) {
if (!(o instanceof Seconds)) return false;
    Seconds __1 =  (Seconds) o;
    return seconds == __1.seconds;
}

  public int hashCode() {
    int h = -660217249;
    h = boostHashCombine(h, _hashCode(seconds));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {seconds}; }

  final double get(){ return seconds(); }
final double getDouble(){ return seconds(); }
double seconds() { return seconds; }
  
  public String toString() { return formatDouble(seconds, 3) + " s"; }
  
  public int compareTo(Seconds s) {
    return cmp(seconds, s.seconds);
  }
  
  Seconds div(double x) { return new Seconds(get()/x); }
  Seconds minus(Seconds x) { return new Seconds(get()-x.get()); }
}
static class ByteBuffer implements Iterable<Byte> {
  byte[] data;
  int size;
  
  ByteBuffer() {}
  ByteBuffer(int size) { if (size != 0) data = new byte[size]; }
  ByteBuffer(Iterable<Byte> l) {
    if (l instanceof Collection) allocate(((Collection) l).size());
    addAll(l);
  }
  ByteBuffer(byte[] data) { this.data = data; size = l(data); }
  // TODO *(ByteBuffer buf) { ... }
  
  void add(int idx, int i) {
    add(0);
    arraycopy(data, idx, data, idx+1, size-(idx+1));
    data[idx] = (byte) i;
  }
  
  void add(int i) { add((byte) i); }
  
  void add(byte i) {
    if (size >= lByteArray(data)) {
      allocate(Math.max(1, toInt(Math.min(maximumSafeArraySize(), lByteArray(data)*2L))));
      if (size >= data.length) throw fail("ByteBuffer too large: " + size);
    }
    data[size++] = i;
  }
  
  void allocate(int n) {
    data = resizeByteArray(data, max(n, size()));
  }
  
  void addAll(Iterable<Byte> l) {
    if (l != null) for (byte i : l) add(i);
  }
  
  final byte[] toByteArray(){ return toArray(); }
byte[] toArray() {
    return size == 0 ? null : resizeByteArray(data, size);
  }
  
  List<Byte> toList() {
    return byteArrayToList(data, 0, size);
  }

  List<Byte> asVirtualList() {
    return new RandomAccessAbstractList<Byte>() {
      public int size() { return size; }
      public Byte get(int i) { return ByteBuffer.this.get(i); }
      public Byte set(int i, Byte val) {
        Byte a = get(i);
        data[i] = val;
        return a;
      }
    };
  }
  
  void reset() { size = 0; }
  void clear() { reset(); }
  
  int size() { return size; }
  boolean isEmpty() { return size == 0; }
  
  byte get(int idx) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    return data[idx];
  }
  
  void set(int idx, byte value) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    data[idx] = value;
  }
  
  byte popLast() {
    if (size == 0) throw fail("empty buffer");
    return data[--size];
  }
  
  // unefficient
  byte popFirst() {
    if (size == 0) throw fail("empty buffer");
    byte b = data[0];
    arraycopy(data, 1, 0, --size);
    return b;
  }
  
  byte last() { return data[size-1]; }
  byte nextToLast() { return data[size-2]; }
  
  public String toString() { return squareBracket(joinWithSpace(toList())); }
  
  public Iterator<Byte> iterator() {
    return new IterableIterator<Byte>() {
      int i = 0;
      
      public boolean hasNext() { return i < size; }
      public Byte next() {
        //if (!hasNext()) fail("Index out of bounds: " + i);
        return data[i++];
      }
    };
  }
  
  /*public ByteIterator byteIterator() {
    ret new ByteIterator {
      int i = 0;
      
      public bool hasNext() { ret i < size; }
      public int next() {
        //if (!hasNext()) fail("Index out of bounds: " + i);
        ret data[i++];
      }
      toString { ret "Iterator@" + i + " over " + ByteBuffer.this; }
    };
  }*/
  
  void trimToSize() {
    data = resizeByteArray(data, size);
  }
  
  int indexOf(byte b) {
    for (int i = 0; i < size; i++)
      if (data[i] == b)
        return i;
    return -1;
  }
  
  byte[] subArray(int start, int end) {
    return subByteArray(data, start, min(end, size));
  }
}
/*sinterface ISleeper extends ISleeper_v2, AutoCloseable {
  void doLater(long targetSysTime, Runnable r); // call only once
}*/



static Class<?> getClass(String name) {
  return _getClass(name);
}

static Class getClass(Object o) {
  return _getClass(o);
}

static Class getClass(Object realm, String name) {
  return _getClass(realm, name);
}


static boolean classIsExportedTo(Class c, java.lang.Module destModule) {
  if (c == null || destModule == null) return false;
  
  java.lang.Module srcModule = c.getModule();
  String packageName = c.getPackageName();
  return srcModule.isExported(packageName, destModule);
}


static boolean isAbstract(Class c) {
  return (c.getModifiers() & Modifier.ABSTRACT) != 0;
}

static boolean isAbstract(Method m) {
  return (m.getModifiers() & Modifier.ABSTRACT) != 0;
}


static boolean reflection_isForbiddenMethod(Method m) {
  return m.getDeclaringClass() == Object.class
    && eqOneOf(m.getName(), "finalize", "clone", "registerNatives");
}


static Set<Class> allInterfacesImplementedBy(Object o) {
  return allInterfacesImplementedBy(_getClass(o));
}

static Set<Class> allInterfacesImplementedBy(Class c) {
  if (c == null) return null;
  HashSet<Class> set = new HashSet();
  allInterfacesImplementedBy_find(c, set);
  return set;
}

static void allInterfacesImplementedBy_find(Class c, Set<Class> set) {
  if (c.isInterface() && !set.add(c)) return;
  do {
    for (Class intf : c.getInterfaces())
      allInterfacesImplementedBy_find(intf, set);
  } while ((c = c.getSuperclass()) != null);
}


static Method findMethod(Object o, String method, Object... args) {
  return findMethod_cached(o, method, args);
}

static boolean findMethod_checkArgs(Method m, Object[] args, boolean debug) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != args.length) {
    if (debug)
      System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
    return false;
  }
  for (int i = 0; i < types.length; i++)
    if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
      if (debug)
        System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
      return false;
    }
  return true;
}


static Method findStaticMethod(Class c, String method, Object... args) {
  Class _c = c;
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (!m.getName().equals(method))
        continue;

      if ((m.getModifiers() & Modifier.STATIC) == 0 || !findStaticMethod_checkArgs(m, args))
        continue;

      return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

static boolean findStaticMethod_checkArgs(Method m, Object[] args) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != args.length)
    return false;
  for (int i = 0; i < types.length; i++)
    if (!(args[i] == null || isInstanceX(types[i], args[i])))
      return false;
  return true;
}



static String unquote(String s) {
  if (s == null) return null;
  if (startsWith(s, '[')) {
    int i = 1;
    while (i < s.length() && s.charAt(i) == '=') ++i;
    if (i < s.length() && s.charAt(i) == '[') {
      String m = s.substring(1, i);
      if (s.endsWith("]" + m + "]"))
        return s.substring(i+1, s.length()-i-1);
    }
  }
  return unquoteSingleOrDoubleQuotes(s);
}


static List<String> quoteAll(String[] l) {
  return quoteAll(asList(l));
}

static List<String> quoteAll(Collection<String> l) {
  List<String> x = new ArrayList();
  for (String s : l)
    x.add(quote(s));
  return x;
}


static int _hashCode(Object a) {
  return a == null ? 0 : a.hashCode();
}


static boolean arraysEqual(Object[] a, Object[] b) {
  if (a.length != b.length) return false;
  for (int i = 0; i < a.length; i++)
    if (neq(a[i], b[i])) return false;
  return true;
}


static Object metaGet(IMeta o, Object key) {
  return metaMapGet(o, key);
}

static Object metaGet(Object o, Object key) {
  return metaMapGet(o, key);
}

static Object metaGet(String key, IMeta o) {
  return metaMapGet(o, key);
}

static Object metaGet(String key, Object o) {
  return metaMapGet(o, key);
}


static Object metaMapGet(IMeta o, Object key) {
  return o == null ? null : o.metaGet(key); // We now let the object itself do it (overridable!)
}

static Object metaMapGet(Object o, Object key) {
  return metaMapGet(toIMeta(o), key);
}


static void metaPut(IMeta o, Object key, Object value) {
  metaMapPut(o, key, value);
}



static void metaPut(Object o, Object key, Object value) {
  metaMapPut(o, key, value);
}


static Map convertObjectMetaToMap(IMeta o) { return convertObjectMetaToMap(o, () -> makeObjectMetaMap()); }
static Map convertObjectMetaToMap(IMeta o, IF0<Map> createEmptyMap) {
  if (o == null) return null;
  
  // The following shortcut depends on the assumption that a meta field never reverts
  // to null when it was a map
  
    Object meta = o._getMeta();
    if (meta instanceof Map) return ((Map) meta);
  
  
  // non-shortcut path (create meta)
   var mutex = tempMetaMutex(o); try {
  var actualMutex = mutex.get();
  synchronized(actualMutex) {
    meta = o._getMeta();
    if (meta instanceof Map) return ((Map) meta);
    Map map = createEmptyMap.get();
    if (meta != null) map.put("previousMeta" , meta);
    o._setMeta(map);
    return map;
  }
} finally { _close(mutex); }}


static <A, B> void syncMapPutOrRemove(Map<A, B> map, A key, B value) {
  syncMapPut2(map, key, value);
}


static float clamp(float x, float a, float b) {
  return x < a ? a : x > b ? b : x;
}

static double clamp(double x, double a, double b) {
  return x < a ? a : x > b ? b : x;
}

static int clamp(int x, int a, int b) {
  return x < a ? a : x > b ? b : x;
}

static long clamp(long x, long a, long b) {
  return x < a ? a : x > b ? b : x;
}


static void add(BitSet bs, int i) {
  bs.set(i);
}

static <A> boolean add(Collection<A> c, A a) {
  return c != null && c.add(a);
}


static void add(Container c, Component x) {
  addToContainer(c, x);
}


static long add(AtomicLong l, long b) {
  return l.addAndGet(b);
}


static <A> A _print(String s, A a) {
  return print(s, a);
}

static <A> A _print(A a) {
  return print(a);
}

static void _print() {
  print();
}


static boolean _eq(Object a, Object b) {
  return eq(a, b);
}


static String toString(Object o) {
  return strOrNull(o);
}


static String formatDouble(double d, int digits) {
  String format = digits <= 0 ? "0" : "0." + rep(digits, '#');
  return decimalFormatEnglish(format, d);
}

static String formatDouble(double d) {
  return str(d);
}




static double ratioToPercent(double x, double y) {
  return x*100/y;
}


static OnePathWithOrigin g22_regionOutline(IImageRegion region) {
  // TODO: optimize
  List<PtBuffer> outlines = g22_allBorderTraces_autoDiagonals(region);
    
  return new OnePathWithOrigin(first(outlines), false);
}


static RuntimeException unimplemented() {
  throw fail("TODO");
}

static RuntimeException unimplemented(String msg) {
  throw fail("TODO: " + msg);
}

static RuntimeException unimplemented(Object obj) {
  throw fail("TODO: implement method in " + className(obj));
}


static <A, B> Map<A, B> putAll(Map<A, B> a, Map<? extends A,? extends B> b) {
  if (a != null && b != null) a.putAll(b);
  return a;
}


static <A, B> MultiMap<A, B> putAll(MultiMap<A, B> a, Map<? extends A,? extends B> b) {
  if (a != null) a.putAll((Map) b);
  return a;
}


static <A, B> Map<A, B> putAll(Map<A, B> a, Object... b) {
  if (a != null)
    litmap_impl(a, b);
  return a;
}



static <A> A getAndClear(IVar<A> v) {
  A a = v.get();
  v.set(null);
  return a;
}


static <A, B> Set<A> keys(Map<A, B> map) {
  return map == null ? new HashSet() : map.keySet();
}

// convenience shortcut for keys_gen
static Set keys(Object map) {
  return keys((Map) map);
}




  static <A, B> Set<A> keys(IMultiMap<A, B> mm) {
    return mm.keySet();
  }





static <A, B> Set<A> keySet(Map<A, B> map) {
  return map == null ? new HashSet() : map.keySet();
}

static Set keySet(Object map) {
  return keys((Map) map);
}




  static <A, B> Set<A> keySet(MultiMap<A, B> mm) {
    return mm.keySet();
  }





static <A, B> int keysSize(MultiMap<A, B> mm) {
  return lKeys(mm);
}


static <A> A reverseGet(List<A> l, int idx) {
  if (l == null || idx < 0) return null;
  int n = l(l);
  return idx < n ? l.get(n-1-idx) : null;
}


static <A, B> Map<A, B> cloneMap(Map<A, B> map) {
  if (map == null) return new HashMap();
  // assume mutex is equal to map
  synchronized(map) {
    return map instanceof TreeMap ? new TreeMap((TreeMap) map) // copies comparator
      : map instanceof LinkedHashMap ? new LinkedHashMap(map)
      : new HashMap(map);
  }
}

static <A, B> List<B> cloneMap(Iterable<A> l, IF1<A, B> f) {
  List x = emptyList(l);
  if (l != null) for (A o : cloneList(l))
    x.add(f.get(o));
  return x;
}


static <A, B> Collection<B> values(Map<A, B> map) {
  return map == null ? emptyList() : map.values();
}

// convenience shortcut for values_gen
static Collection values(Object map) {
  return values((Map) map);
}


static <A, B> Collection<B> values(MultiMap<A, B> mm) {
  return mm == null ? emptyList() : concatLists(values(mm.data));
}





static <A, B, C extends Collection<B>> List<B> allValues(Map<A, C> map) {
  List<B> out = new ArrayList();
  for (var l : values(map))
    addAll(out, l);
  return out;
}


static <A> List<A> concatLists(Iterable<A>... lists) {
  List<A> l = new ArrayList();
  if (lists != null) for (Iterable<A> list : lists)
    addAll(l, list);
  return l;
}

static <A> List<A> concatLists(Collection<? extends Iterable<A>> lists) {
  List<A> l = new ArrayList();
  if (lists != null) for (Iterable<A> list : lists)
    addAll(l, list);
  return l;
}



static <A> A set(A o, String field, Object value) {
  if (o == null) return null;
  if (o instanceof Class) set((Class) o, field, value);
  else try {
    Field f = set_findField(o.getClass(), field);
    makeAccessible(f);
    smartSet(f, o, value);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
  return o;
}

static void set(Class c, String field, Object value) {
  if (c == null) return;
  try {
    Field f = set_findStaticField(c, field);
    makeAccessible(f);
    smartSet(f, null, value);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}
  
static Field set_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Static field '" + field + "' not found in " + c.getName());
}

static Field set_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Field '" + field + "' not found in " + c.getName());
}

static void set(BitSet bs, int idx) {
  { if (bs != null) bs.set(idx); }
}


static boolean hasNext(Iterator it) {
  return it != null && it.hasNext();
}


static Method hashMap_findKey_method;

static <A, B> A hashMap_findKey(HashMap<A, B> map, Object key) { try {
  if (hashMap_findKey_method == null)
    hashMap_findKey_method = findMethodNamed(HashMap.class, "getNode");
  Map.Entry<A, B> entry = (Map.Entry) hashMap_findKey_method.invoke(map, hashMap_internalHash(key), key);
  // java.util.Map.Entry<A, B> entry = (java.util.Map.Entry) call(hash, 'getNode, hashMap_internalHash(key), wkey);
  return entry == null ? null : entry.getKey();
} catch (Exception __e) { throw rethrow(__e); } }


static String find(String pattern, String text) {
  Matcher matcher = Pattern.compile(pattern).matcher(text);
  if (matcher.find())
    return matcher.group(1);
  return null;
}

static <A> A find(Collection<A> c, Object... data) {
  for (A x : c)
    if (checkFields(x, data))
      return x;
  return null;
}


static String a(String noun) {
  if (eq(noun, "")) return "?";
  return ("aeiou".indexOf(noun.charAt(0)) >= 0 ? "an " : "a ") + noun;
}

static String a(String contents, Object... params) {
  return hfulltag("a", contents, params);
}



static String b(Object contents, Object... params) {
  return fulltag("b", contents, params);
}


static int hashCodeFor(Object a) {
  return a == null ? 0 : a.hashCode();
}


static String joinNemptiesWithColon(String... strings) {
  return joinNempties(": ", strings);
}

static String joinNemptiesWithColon(Collection<String> strings) {
  return joinNempties(": ", strings);
}


static String commaCombine(Object... l) {
  return joinNemptiesWithComma(flattenCollectionsAndArrays(l));
}


static int boostHashCombine(int a, int b) {
  return a ^ (b + 0x9e3779b9 + (a << 6) + (a >>> 2));
  
  // OLD (changed) 2022/3/10: ret a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2));
}


static WidthAndHeight widthAndHeight(BufferedImage image) {
  return image == null ? null : widthAndHeight(image.getWidth(), image.getHeight());
}

static WidthAndHeight widthAndHeight(int w) { return widthAndHeight(w, w); }
static WidthAndHeight widthAndHeight(int w, int h) {
  return new WidthAndHeightFinal(w, h);
}


// brightness: 0 to 255
static int rgbIntFromGrayscale(int brightness) {
  brightness = clampToUByte(brightness);
  return brightness | (brightness << 8) | (brightness << 16);
}

// brightness: 0 to 1
static int rgbIntFromGrayscale(double brightness) {
  return rgbIntFromGrayscale(zeroToOneToZeroTo255(brightness));
}


static int getInt(List c, int i) {
  return toInt(get(c, i));
}

static int getInt(Map map, Object key) {
  return toInt(mapGet(map, key));
}

static int getInt(Object o, String field) {
  return toInt(getOpt(o, (String) field));
}

static int getInt(String field, Object o) {
  return getInt(o, field);
}


static BufferedImage grayImageFromIBWImage(IBWImage img) {
  int w = img.getWidth(), h = img.getHeight();
  byte[] pixels = new byte[w*h];
  int i = 0;
  for (int y = 0; y < h; y++)
    for (int x = 0; x < w; x++) {
      int pixel = iround(img.getFloatPixel(x, y)*255); // tODO: is it round or floor?
      
      pixels[i++] = clampToUByte(pixel);
    }
  return newGrayBufferedImage(w, h, pixels);
}


static BWImage iBWImageToBWImage(IBWImage img) {
  int w = img.getWidth(), h = img.getHeight();
  BWImage out = new BWImage(w, h);
  for (int y = 0; y < h; y++) for (int x = 0; x < w; x++) out.setPixel(x, y, img.getFloatPixel(x, y));
  return out;
}


static double sqrt(double x) {
  return Math.sqrt(x);
}


static Pt ptMinus(Pt a, Pt b) {
  if (b == null) return a;
  return new Pt(a.x-b.x, a.y-b.y);
}


static UnsupportedOperationException unsupportedOperation() {
  throw new UnsupportedOperationException();
}


static int rgbRed(int rgb) {
  return (rgb >> 16) & 0xFF;
}


static int rgbGreen(int rgb) {
  return (rgb >> 8) & 0xFF;
}


static int rgbBlue(int rgb) {
  return rgb & 0xFF;
}



  static float clampZeroToOne(float x) {
    return x < 0 ? 0 : x > 1 ? 1 : x;
  }


  static double clampZeroToOne(double x) {
    return x < 0 ? 0 : x > 1 ? 1 : x;
  }




static int rgbInt(int r, int g, int b) {
  return (clamp(r, 0, 255) << 16) | (clamp(g, 0, 255) << 8) | clamp(b, 0, 255);
}

static int rgbInt(byte r, byte g, byte b) {
  return (ubyteToInt(r) << 16) | (ubyteToInt(g) << 8) | ubyteToInt(b);
}


static int asInt(Object o) {
  return toInt(o);
}


static String spaceCombine(Object... l) {
  return joinNemptiesWithSpace(flattenCollections(ll(l)));
}


static int lIntArray(int[] a) {
  return a == null ? 0 : a.length;
}


static int[] resizeIntArray(int[] a, int n) {
  if (n == lIntArray(a)) return a;
  int[] b = new int[n];
  arraycopy(a, 0, b, 0, Math.min(lIntArray(a), n));
  return b;
}


static int maximumSafeArraySize() {
  return Integer.MAX_VALUE-8;
}


static Object[] toArray(Collection c) {
  return toObjectArray(c);
}

static <A> A[] toArray(Class<A> type, Iterable<A> c) {
  return toArray(c, type);
}

static <A> A[] toArray(Class<A> type, Collection<A> c) {
  return toArray(c, type);
}

static <A> A[] toArray(Collection<A> c, Class<A> type) {
  A[] a = arrayOfType(l(c), type);
  if (a.length == 0) return a;
  asList(c).toArray(a);
  return a;
}

static <A> A[] toArray(Iterable<A> c, Class<A> type) {
  var c2 = asList(c);
  A[] a = arrayOfType(l(c2), type);
  if (a.length == 0) return a;
  c2.toArray(a);
  return a;
}

// array must have correct length and will be filled
static <A> A[] toArray(A[] array, Collection c) {
  if (array == null || c == null) return null;
  asList(c).toArray(array);
  return array;
}


static int[] subIntArray(int[] b, int start) {
  return subIntArray(b, start, l(b));
}
  
static int[] subIntArray(int[] b, int start, int end) {
  start = max(start, 0); end = min(end, l(b));
  if (start == 0 && end == l(b)) return b;
  if (start >= end) return new int[0];
  int[] x = new int[end-start];
  System.arraycopy(b, start, x, 0, end-start);
  return x;
}




static <A> List<A> asVirtualList(A[] a) {
  return wrapArrayAsList(a);
}


static String squareBracket(String s) {
  return "[" + s + "]";
}


static int getWidth(Component c) {
  return c == null ? 0 : (int) swingCall(c, "getWidth");
}


static int getHeight(Component c) {
  return c == null ? 0 : (int) swingCall(c, "getHeight");
}


static Rect rect(int x, int y, int w, int h) {
  return new Rect(x, y, w, h);
}

static Rect rect(Pt p, int w, int h) {
  return new Rect(p.x, p.y, w, h);
}

static Rect rect(int w, int h) {
  return new Rect(0, 0, w, h);
}




static long longMul(long a, long b) {
  return a*b;
}


static String flexLines(Object... l) {
  return lines(flattenIterablesAndArrays(ll(l)));
}


static String roundBracket(String s) {
  return "(" + s + ")";
}

static String roundBracket(Object s) {
  return roundBracket(str(s));
}


static List<Integer> countIteratorToList(int b) { return countIteratorToList(0, b); }
static List<Integer> countIteratorToList(int a, int b) {
  return asList(countIterator(a, b));
}





static <A> List<A> countIteratorToList(int b, IF1<Integer, A> f) { return countIteratorToList(0, b, f); }
static <A> List<A> countIteratorToList(int a, int b, IF1<Integer, A> f) {
  return asList(countIterator(a, b, f));
}



static List<Integer> countIteratorToList(int a, int b, int step) {
  return asList(countIterator(a, b, step));
}



static <A> List<A> countIteratorToList(double a, double b, double step, IF1<Double, A> f) {
  return asList(countIterator(a, b, step, f));
}



static <A> List<Double> countIteratorToList(double a, double b, double step) {
  return asList(countIterator(a, b, step));
}



static <A> List<A> countIteratorToList(IF1<Double, A> f, double a, double b, double step) {
  return asList(countIterator(f, a, b, step));
}

static <A> List<A> countIteratorToList(IF1<Integer, A> f, int b) { return countIteratorToList(f, 0, b); }
static <A> List<A> countIteratorToList(IF1<Integer, A> f, int a, int b) {
  return asList(countIterator(f, a, b));
}


// lineNr starts at 1
static String getLine(String s, int lineNr) {
  return safeGet(toLines(s), lineNr-1);
}


static byte[] cloneByteArray(byte[] a) {
  if (a == null) return null;
  byte[] b = new byte[a.length];
  System.arraycopy(a, 0, b, 0, a.length);
  return b;
}


static BWImage toBW(RGBImage img) {
  return img == null ? null : new BWImage(img);
}


static int getPixel(BufferedImage img, int x, int y) {
  return img.getRGB(x, y);
}

static int getPixel(BufferedImage img, Pt p) {
  return img.getRGB(p.x, p.y);
}


static String str_px(int w, int h) {
  return n2(w) + "*" + n2(h) + "px";
}

static String str_px(WidthAndHeight image) {
  return image == null ? null : str_px(image.getWidth(), image.getHeight());
}


static double doubleRatio(double x, double y) {
  return y == 0 ? 0 : x/y;
}


static double doubleRatio(Seconds x, Seconds y) {
  return doubleRatio(x.get(), y.get());
}



static int bitCount(BitSet bs) {
  return bs == null ? 0 : bs.cardinality();
}

static int bitCount(int i) {
  return Integer.bitCount(i);
}

static int bitCount(byte[] array) {
  if (array == null) return 0;
  int sum = 0;
  for (var b : array)
    sum += bitCount(ubyteToInt(b));
  return sum;
}


static volatile int numberOfCores_value;

static int numberOfCores() {
  if (numberOfCores_value == 0)
    numberOfCores_value = Runtime.getRuntime().availableProcessors();
  return numberOfCores_value;
}


// runnable = Runnable or String (method name)
static Thread newThread(Object runnable) {
  return new BetterThread(_topLevelErrorHandling(toRunnable(runnable)));
}

static Thread newThread(Object runnable, String name) {
  if (name == null) name = defaultThreadName();
  return new BetterThread(_topLevelErrorHandling(toRunnable(runnable)), name);
}

static Thread newThread(String name, Object runnable) {
  return newThread(runnable, name);
}


static int random(int n) { return random(n, defaultRandomGenerator()); }
static int random(int n, Random r) {
  return random(r, n);
}

static long random(long n) { return random(n, defaultRandomGenerator()); }
static long random(long n, Random r) {
  return random(r, n);
}

static int random(Random r, int n) {
  return n <= 0 ? 0 : getRandomizer(r).nextInt(n);
}

static long random(Random r, long n) {
  return n <= 0 ? 0 : getRandomizer(r).nextLong(n);
}

static double random(double max) {
  return random()*max;
}

static double random() {
  return defaultRandomGenerator().nextInt(100001)/100000.0;
}

static double random(double min, double max) {
  return min+random()*(max-min);
}

// min <= value < max
static int random(int min, int max) {
  return min+random(max-min);
}

// min <= value < max
static long random(long min, long max) {
  return min+random(max-min);
}

static int random(int min, int max, Random r) {
  return random(r, min, max);
}

static int random(Random r, int min, int max) {
  return min+random(r, max-min);
}

static <A> A random(List<A> l) {
  return oneOf(l);
}

static <A> A random(Collection<A> c) {
  if (c instanceof List) return random((List<A>) c);
  int i = random(l(c));
  return collectionGet(c, i);
}







static <A, B> Pair<A, B> random(Map<A, B> map) {
  return entryToPair(random(entries(map)));
}


static <A> A popFirst(List<A> l) {
  if (empty(l)) return null;
  A a = first(l);
  l.remove(0);
  return a;
}

static <A> A popFirst(Collection<A> l) {
  if (empty(l)) return null;
  A a = first(l);
  l.remove(a);
  return a;
}

static <A, B> Pair<A, B> popFirst(Map<A, B> map) {
  if (map == null) return null;
  var it = map.entrySet().iterator();
  if (!it.hasNext()) return null;
  var p = mapEntryToPair(it.next());
  it.remove();
  return p;
}

static <A> List<A> popFirst(int n, List<A> l) {
  List<A> part = cloneSubList(l, 0, n);
  removeSubList(l, 0, n);
  return part;
}

static <A> AppendableChain<A> popFirst(AppendableChain<A> a) {
  return a == null ? null : a.popFirst();
}


// Yes the nomenclature is a bit illogical

static <A> Chain<A> chainPlus(Chain<A> chain, A a) {
  return new Chain<A>(a, chain);
}

static <A> Chain<A> chainPlus(Chain<A> chain, A... l) {
  for (A a : unnullForIteration(l))
    chain = chainPlus(chain, a);
  return chain;
}

static <A> ReverseChain<A> chainPlus(ReverseChain<A> chain, A a) {
  return new ReverseChain<A>(chain, a);
}

static <A> ReverseChain<A> chainPlus(ReverseChain<A> chain, A... l) {
  for (A a : unnullForIteration(l))
    chain = chainPlus(chain, a);
  return chain;
}


static <A> AppendableChain<A> chainPlus(AppendableChain<A> chain, A a) {
  if (chain == null) return new AppendableChain<A>(a);
  chain.add(a);
  return chain;
}

static <A> AppendableChain<A> chainPlus(AppendableChain<A> chain, A... l) {
  for (A a : unnullForIteration(l))
    chain = chainPlus(chain, a);
  return chain;
}




static void syncNotifyAll(Object o) {
  if (o != null) synchronized(o) { o.notifyAll(); }
}


static void fillArrayUnlessZero(byte[] a, byte value) {
  if (value != 0) Arrays.fill(a, value);
}

static void fillArrayUnlessZero(int[] a, int value) {
  if (value != 0) Arrays.fill(a, value);
}

static void fillArrayUnlessZero(float[] a, float value) {
  if (value != 0) Arrays.fill(a, value);
}


static boolean inRange(int x, int n) {
  return x >= 0 && x < n;
}

static boolean inRange(int x, List l) {
  return inRange(x, l(l));
}

static boolean inRange(int x, int a, int b) {
  return x >= a && x < b;
}


static int limitToUByte(int i) {
  return max(0, min(255, i));
}


static BufferedImage bufferedImage(int[] pixels, int w, int h) {
  return intArrayToBufferedImage(pixels, w, h);
}

static BufferedImage bufferedImage(int[] pixels, WidthAndHeight size) {
  return bufferedImage(pixels, size.getWidth(), size.getHeight());
}

static BufferedImage bufferedImage(int w, int h, int[] pixels) {
  return intArrayToBufferedImage(pixels, w, h);
}

// undefined color, seems to be all black in practice
static BufferedImage bufferedImage(int w, int h) {
  return newBufferedImage(w, h);
}


static BufferedImage bufferedImage(int w, int h, RGB rgb) {
  return newBufferedImage(w, h, rgb);
}



static BufferedImage bufferedImage(int w, Color color) { return bufferedImage(w, w, color); }
static BufferedImage bufferedImage(int w, int h, Color color) {
  return newBufferedImage(w, h, color);
}


static BufferedImage bufferedImage(Pt p, Color color) {
  return newBufferedImage(p, color);
}

static BufferedImage bufferedImage(WidthAndHeight size, Color color) {
  return newBufferedImage(size.w(), size.h(), color);
}

static BufferedImage bufferedImage(Color color, WidthAndHeight size) {
  return bufferedImage(size, color);
}


static <A> IterableIterator<A> filterI(Iterator<A> it, F1<A, Boolean> f) {
  return filterIterator(it, f);
}



static <A> IterableIterator<A> filterI(Iterator<A> it, IF1<A, Boolean> f) {
  return filterIterator(it, f);
}



static <A> IterableIterator<A> filterI(F1<A, Boolean> f, Iterator<A> it) {
  return filterIterator(f, it);
}

static <A> IterableIterator<A> filterI(IF1<A, Boolean> f, Iterator<A> it) {
  return filterIterator(f, it);
}

static <A> IterableIterator<A> filterI(IF1<A, Boolean> f, Iterable<A> it) {
  return filterIterator(f, iterator(it));
}


static Pt origin() {
  return pt(0, 0);
}


static <A> List<A> reversedList(Iterable<A> l) {
  List<A> x = cloneList(l);
  Collections.reverse(x);
  return x;
}


static java.util.Timer doLater(long delay, final Object r) {
  ping();
  final java.util.Timer timer = new java.util.Timer();
  timer.schedule(timerTask(r, timer), delay);
  return vmBus_timerStarted(timer);
}

static java.util.Timer doLater(double delaySeconds, final Object r) {
  return doLater(toMS(delaySeconds), r);
}


static Timestamp sysTimeToTimestamp(long now) {
  return now == 0 ? null : new Timestamp(now - clockToSysTimeDiff());
}


static Timestamp tsNow() {
  return new Timestamp();
}


static <A, B> MultiSetMap<A, B> treeMultiSetMap() {
  return new MultiSetMap(true);
}

static <A, B> MultiSetMap<A, B> treeMultiSetMap(Comparator<A> comparator) {
  return new MultiSetMap(new TreeMap<A, Set<B>>(comparator));
}


static <A, B> B firstValue(Map<A, B> map) {
  return first(values(map));
}


static <A, B> B firstValue(MultiSetMap<A, B> map) {
  return map == null ? null : first(firstValue(map.data));
}



static <A, B> B firstValue(MultiMap<A, B> map) {
  return map == null ? null : first(firstValue(map.data));
}



static <A, B> A firstKey(Map<A, B> map) {
  return first(keys(map));
}


static <A, B> A firstKey(IMultiMap<A, B> map) {
  return map == null ? null : first(map.keySet());
}



static GrabbableIntPixels grabbableIntPixels_fastOrSlow(BufferedImage image) { try {
  try {
    GrabbableIntPixels gp = grabbableIntPixels(image);
    if (gp != null) return gp;
  } catch (Throwable __e) { pcallFail(__e); }
    
  // TODO: use GrabbableRGBBytePixels and convert manually
  // - should be way faster than PixelGrabber
  
  int w = image.getWidth(), h = image.getHeight();
  int[] data = new int[w*h];
  PixelGrabber pixelGrabber = new PixelGrabber(image, 0, 0, w, h, data, 0, w);
  if (!pixelGrabber.grabPixels())
    throw fail("Could not grab pixels");
      
  return new GrabbableIntPixels(data, w, h, 0, w);
} catch (Exception __e) { throw rethrow(__e); } }


static void arrayCopy(Object[] a, Object[] b) {
  arraycopy(a, b);
}



static void arrayCopy(Object src, Object dest, int destPos, int n) { arrayCopy(src, 0, dest, destPos, n); }
static void arrayCopy(Object src, int srcPos, Object dest, int destPos, int n) {
  arraycopy(src, srcPos, dest, destPos, n);
}


static BufferedImage toBufferedImage(Object o) {
  return toBufferedImageOpt(o);
}


static void saveImage(File f, BufferedImage img) {
  if (hasJPEGExtension(f))
    saveJPG(f, img);
  else
    savePNG(f, img);
}

static void saveImage(BufferedImage img, File f) {
  saveImage(f, img);
}


static void setPixel(BufferedImage img, int p_x, int p_y, Color color) { setPixel(img, pt(p_x, p_y), color); }

static void setPixel(BufferedImage img, Pt p, Color color) {
  { if (img != null) img.setRGB(p.x, p.y, colorToIntOpaque(color)); }
}

static void setPixel(Graphics2D g, int p_x, int p_y, Color color) { setPixel(g, pt(p_x, p_y), color); }

static void setPixel(Graphics2D g, Pt p, Color color) {
  g.setColor(color);
  g.drawRect(p.x, p.y, 1, 1);
}


static long now_virtualTime;
static long now() {
  return now_virtualTime != 0 ? now_virtualTime : System.currentTimeMillis();
}





static String formatLocalDateWithSeconds(long time) {
  return localDateWithSeconds(time);
}



static String formatLocalDateWithSeconds() {
  return localDateWithSeconds();
}


static BigInteger plus(BigInteger a, BigInteger b) {
  return a.add(b);
}

static BigInteger plus(BigInteger a, long b) {
  return a.add(bigint(b));
}

static long plus(long a, long b) { return a+b; }
static int plus(int a, int b) { return a+b; }
static float plus(float a, float b) { return a+b; }
static double plus(double a, double b) { return a+b; }


static long toMS(double seconds) {
  return (long) (seconds*1000);
}

static long toMS(Duration d) {
  return d == null ? 0 : d.toMillis();
}


static long clockTimeToSystemTime(long now) {
  return now == 0 ? 0 : now + clockToSysTimeDiff();
}


static <A> List<A> minus(Collection<A> a, Object... b) {
  Set set = asSet(b);
  List l = new ArrayList();
  for (Object s : unnull(a))
    if (!set.contains(s))
      l.add(s);
  return l;
}

static BigInteger minus(BigInteger a, BigInteger b) {
  return a.subtract(b);
}


static Complex minus(Complex c) {
  return c == null ? null : complex(-c.re(), -c.im());
}



  static int minus(int a, int b) {
    return a-b;
  }
  
  static int minus(int a) {
    return -a;
  }


  static double minus(double a, double b) {
    return a-b;
  }
  
  static double minus(double a) {
    return -a;
  }


  static long minus(long a, long b) {
    return a-b;
  }
  
  static long minus(long a) {
    return -a;
  }




static int parseDigit(char c) {
  return c >= '0' && c <= '9' ? c-'0' : 0;
}

static int parseDigit(String s, int i) {
  return parseDigit(s.charAt(i));
}


static String singleDigitBytesToString(ByteBuffer l) {
  if (l == null) return null;
  int n = l.size();
  char[] data = new char[n];
  for (int i = 0; i < n; i++)
    data[i] = (char) ('0' + ubyteToInt(l.get(i)) % 10);
  return str(data);
}


static int length(Object[] array) {
  return array == null ? 0 : array.length;
}

static int length(List list) {
  return list == null ? 0 : list.size();
}

static int length(String s) {
  return s == null ? 0 : s.length();
}


static Pt translatePt(Pt a, Pt b) {
  return addPts(a, b);
}

static Pt translatePt(int x, int y, Pt a) {
  return addPts(a, pt(x, y));
}

static Pt translatePt(Pt a, int x, int y) {
  return translatePt(x, y, a);
}


static PtBuffer ptBuffer(Iterable<Pt> l) {
  return new PtBuffer(l);
}




static final Pt[] onePathDirections_directions = {
  pt(0, 0),
  pt(-1, -1),
  pt(0, -1),
  pt(1, -1),
  pt(1, 0),
  pt(1, 1),
  pt(0, 1),
  pt(-1, 1),
  pt(-1, 0)
};

static Pt[] onePathDirections() { return onePathDirections_directions; }


static <A> A last(List<A> l) {
  return empty(l) ? null : l.get(l.size()-1);
}

static char last(String s) {
  return empty(s) ? '#' : s.charAt(l(s)-1);
}

static byte last(byte[] a) {
  return l(a) != 0 ? a[l(a)-1] : 0;
}


  static int last(int[] a) {
    return l(a) != 0 ? a[l(a)-1] : 0;
  }


  static long last(long[] a) {
    return l(a) != 0 ? a[l(a)-1] : 0;
  }



static double last(double[] a) {
  return l(a) != 0 ? a[l(a)-1] : 0;
}

static <A> A last(A[] a) {
  return l(a) != 0 ? a[l(a)-1] : null;
}

static <A> A last(Iterator<A> it) {
  A a = null;
  while  (it.hasNext()) { ping(); a = it.next(); }
  return a;
}

static <A> A last(Collection<A> l) {
  if (l == null) return null;
  if (l instanceof List) return (A) last((List) l);
  if (l instanceof SortedSet) return (A) last((SortedSet) l);
  Iterator<A> it = iterator(l);
  A a = null;
  while  (it.hasNext()) { ping(); a = it.next(); }
  return a;
}

static <A> A last(SortedSet<A> l) {
  return l == null ? null : l.last();
}


static <A> A last(ReverseChain<A> l) {
  return l == null ? null : l.element;
}



static int last(IntBuffer buf) {
  return buf.get(buf.size()-1);
}



static byte last(ByteBuffer buf) {
  return buf.get(buf.size()-1);
}









static long last(LongBuffer l) {
  return l.last();
}







static <A> A last(CompactLinkedHashSet<A> set) {
  return set == null ? null : set.last();
}



static int onePathLookupDirection(Pt p) {
  return indexOf(onePathDirections(), p);
}



  static void assertBetween(long a, long b, long x) { assertBetween("", a, b, x); }
static void assertBetween(String msg, long a, long b, long x) {
    { if (x >= a && x <= b) return; }
    throw fail(colonCombine(msg, x + " is not between " + a + " and " + b));
  }


  static void assertBetween(int a, int b, int x) { assertBetween("", a, b, x); }
static void assertBetween(String msg, int a, int b, int x) {
    { if (x >= a && x <= b) return; }
    throw fail(colonCombine(msg, x + " is not between " + a + " and " + b));
  }


  static void assertBetween(double a, double b, double x) { assertBetween("", a, b, x); }
static void assertBetween(String msg, double a, double b, double x) {
    { if (x >= a && x <= b) return; }
    throw fail(colonCombine(msg, x + " is not between " + a + " and " + b));
  }




static Rect boundsOfPts(Iterable<Pt> l) {
  BoundsFinder bf = new BoundsFinder();
  for (var p : unnullForIteration(l)) bf.add(p);
  return bf.get();
}


static Image2B toImage2B(BufferedImage img) {
  return img == null ? null : new Image2B(img);
}

static Image2B toImage2B(MakesBufferedImage img) {
  if (img == null) return null;
  if (img instanceof Image2B) return ((Image2B) img);
  if (img instanceof BWImage) return new Image2B((BWImage) img);
  if (img instanceof IBinaryImage) return iBinaryImageToImage2B((IBinaryImage) img);
  return new Image2B(toBufferedImage(img));
}


static Image2B iBinaryImageToImage2B(IBinaryImage img) {
  if (img == null) return null;
  if (img instanceof Image2B) return ((Image2B) img);
  int w = img.getWidth(), h = img.getHeight();
  byte[] pixels = new byte[(w*h+7)/8];
  int i = 0;
  for (int y = 0; y < h; y++)
    for (int x = 0; x < w; x++) {
      if (img.getBoolPixel(x, y))
        pixels[i/8] |= 1 << (i & 7);
      i++;
    }
    
  return new Image2B(w, h, pixels);
}


static Set emptySet() {
  return new HashSet();
}


static <A, B> Map.Entry<A, B> firstEntry(Map<A, B> map) {
  return empty(map) ? null : first(map.entrySet());
}


static long sysNow() {
  ping();
  return System.nanoTime()/1000000;
}


static Thread startThread(Object runnable) {
  return startThread(defaultThreadName(), runnable);
}

static Thread startThread(String name, Runnable runnable) {
  runnable = wrapAsActivity(runnable);
  return startThread(newThread(runnable, name));
}

static Thread startThread(String name, Object runnable) {
  runnable = wrapAsActivity(runnable);
  return startThread(newThread(toRunnable(runnable), name));
}

static Thread startThread(Thread t) {
  
  _registerThread(t);
  
  t.start();
  return t;
}


static java.util.Timer doLater_daemon(long delay, final Object r) {
  final java.util.Timer timer = new java.util.Timer(true);
  timer.schedule(timerTask(r, timer), delay);
  return timer;
}

static java.util.Timer doLater_daemon(double delaySeconds, final Object r) {
  return doLater_daemon(toMS(delaySeconds), r);
}



static void cancelTimer(javax.swing.Timer timer) {
  if (timer != null) timer.stop();
}


static void cancelTimer(java.util.Timer timer) {
  if (timer != null) timer.cancel();
}

static void cancelTimer(Object o) {
  if (o instanceof java.util.Timer) cancelTimer((java.util.Timer) o);
  
  else if (o instanceof javax.swing.Timer) cancelTimer((javax.swing.Timer) o);
  
  else if (o instanceof AutoCloseable) { try { ((AutoCloseable) o).close(); } catch (Throwable __e) { pcallFail(__e); }}
}


static int seconds() {
  return seconds(java.util.Calendar.getInstance());
}

static int seconds(java.util.Calendar c) {
  return c.get(java.util.Calendar.SECOND);
}


static int lByteArray(byte[] a) {
  return a == null ? 0 : a.length;
}


static byte[] resizeByteArray(byte[] a, int n) {
  if (n == l(a)) return a;
  byte[] b = new byte[n];
  arraycopy(a, 0, b, 0, min(l(a), n));
  return b;
}


static <A> ArrayList<Byte> byteArrayToList(byte[] a) {
  if (a == null) return null;
  return byteArrayToList(a, 0, a.length);
}

// no range checking on from/to in the interest of speed
static <A> ArrayList<Byte> byteArrayToList(byte[] a, int from, int to) {
  if (a == null) return null;
  ArrayList < Byte > l = new ArrayList<>(to-from);
  for (int i = from; i < to; i++) l.add(a[i]);
  return l;
}


static <A> A popLast(List<A> l) {
  return liftLast(l);
}

static <A> List<A> popLast(int n, List<A> l) {
  return liftLast(n, l);
}




static <A> A nextToLast(List<A> l) {
  return get(l, l(l)-2);
}


static byte[] subByteArray(byte[] b, int start) {
  return subByteArray(b, start, l(b));
}
  
static byte[] subByteArray(byte[] b, int start, int end) {
  start = max(start, 0); end = min(end, l(b));
  if (start == 0 && end == l(b)) return b;
  if (start >= end) return new byte[0];
  byte[] x = new byte[end-start];
  System.arraycopy(b, start, x, 0, end-start);
  return x;
}






static boolean eqOneOf(Object o, Object... l) {
  if (l != null) for (Object x : l) if (eq(o, x)) return true; return false;
}


static Method findMethod_cached(Object o, String method, Object... args) { try {
  if (o == null) return null;
  if (o instanceof Class) {
    _MethodCache cache = callOpt_getCache((Class) o);
    List<Method> methods = cache.cache.get(method);
    if (methods != null) for (Method m : methods)
      if (isStaticMethod(m) && findMethod_checkArgs(m, args, false))
        return m;
    return null;
  } else {
    _MethodCache cache = callOpt_getCache(o.getClass());
    List<Method> methods = cache.cache.get(method);
    if (methods != null) for (Method m : methods)
      if (findMethod_checkArgs(m, args, false))
        return m;
    return null;
  }
} catch (Exception __e) { throw rethrow(__e); } }



static String unquoteSingleOrDoubleQuotes(String s) {
  if (s == null) return null;
  if (s.length() > 1) {
    char c = s.charAt(0);
    if (c == '\"' || c == '\'') {
      int l = endsWith(s, c) ? s.length()-1 : s.length();
      StringBuilder sb = new StringBuilder(l-1);
  
      for (int i = 1; i < l; i++) {
        char ch = s.charAt(i);
        if (ch == '\\') {
          char nextChar = (i == l - 1) ? '\\' : s.charAt(i + 1);
          // Octal escape?
          if (nextChar >= '0' && nextChar <= '7') {
              String code = "" + nextChar;
              i++;
              if ((i < l - 1) && s.charAt(i + 1) >= '0'
                      && s.charAt(i + 1) <= '7') {
                  code += s.charAt(i + 1);
                  i++;
                  if ((i < l - 1) && s.charAt(i + 1) >= '0'
                          && s.charAt(i + 1) <= '7') {
                      code += s.charAt(i + 1);
                      i++;
                  }
              }
              sb.append((char) Integer.parseInt(code, 8));
              continue;
          }
          switch (nextChar) {
          case '\"': ch = '\"'; break;
          case '\\': ch = '\\'; break;
          case 'b': ch = '\b'; break;
          case 'f': ch = '\f'; break;
          case 'n': ch = '\n'; break;
          case 'r': ch = '\r'; break;
          case 't': ch = '\t'; break;
          case '\'': ch = '\''; break;
          // Hex Unicode: u????
          case 'u':
              if (i >= l - 5) {
                  ch = 'u';
                  break;
              }
              int code = Integer.parseInt(
                      "" + s.charAt(i + 2) + s.charAt(i + 3)
                         + s.charAt(i + 4) + s.charAt(i + 5), 16);
              sb.append(Character.toChars(code));
              i += 5;
              continue;
          default:
            ch = nextChar; // added by Stefan
          }
          i++;
        }
        sb.append(ch);
      }
      return sb.toString();
    }
  }
    
  return s; // not quoted - return original
}


static IMeta toIMeta(Object o) {
  return initIMeta(o);
}


static Map makeObjectMetaMap() {
  //ret synchroLinkedHashMap();
  return new CompactHashMap();
}


static IAutoCloseableF0 tempMetaMutex(IMeta o) {
  return o == null ? null : o._tempMetaMutex();
}


static void _close(AutoCloseable c) {
  if (c != null) try {
    c.close();
  } catch (Throwable e) {
    // Some classes stupidly throw an exception on double-closing
    if (c instanceof javax.imageio.stream.ImageOutputStream)
      return;
    else throw rethrow(e);
  }
}


static <A, B> void syncMapPut2(Map<A, B> map, A key, B value) {
  if (map != null && key != null) synchronized(collectionMutex(map)) {
    if (value != null) map.put(key, value);
    else map.remove(key);
  }
}


static void addToContainer(Container a, Component... b) {
  if (a == null) return;
  { swing(() -> { 
    for (Component c : unnullForIteration(b))
      if (c != null) 
        a.add(c);
  }); }
}


static String rep(int n, char c) {
  return repeat(c, n);
}

static String rep(char c, int n) {
  return repeat(c, n);
}

static <A> List<A> rep(A a, int n) {
  return repeat(a, n);
}

static <A> List<A> rep(int n, A a) {
  return repeat(n, a);
}



static String decimalFormatEnglish(String format, double d) {
  return decimalFormatEnglish(format).format(d);
}

static java.text.DecimalFormat decimalFormatEnglish(String format) {
  return new java.text.DecimalFormat(format, new java.text.DecimalFormatSymbols(Locale.ENGLISH));
}


static List<PtBuffer> g22_allBorderTraces_autoDiagonals(IImageRegion region) {
  return region.createdWithDiagonals()
    ? g22_allBorderTraces_withDiagonals(region)
    : g22_allBorderTraces(region);
}


static HashMap litmap(Object... x) {
  HashMap map = new HashMap();
  litmap_impl(map, x);
  return map;
}

static void litmap_impl(Map map, Object... x) {
  if (x != null) for (int i = 0; i < x.length-1; i += 2)
    if (x[i+1] != null)
      map.put(x[i], x[i+1]);
}


static <A, B> int lKeys(MultiMap<A, B> mm) {
  return mm == null ? 0 : mm.keysSize();
}


// This is a bit rough... finds static and non-static methods.

static Method findMethodNamed(Object obj, String method) {
  if (obj == null) return null;
  if (obj instanceof Class)
    return findMethodNamed((Class) obj, method);
  return findMethodNamed(obj.getClass(), method);
}

static Method findMethodNamed(Class c, String method) {
  while (c != null) {
    for (Method m : c.getDeclaredMethods())
      if (m.getName().equals(method)) {
        makeAccessible(m);
        return m;
      }
    c = c.getSuperclass();
  }
  return null;
}


static int hashMap_internalHash(Object key) {
  int h;
  return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);
}


static boolean checkFields(Object x, Object... data) {
  for (int i = 0; i < l(data); i += 2)
    if (neq(getOpt(x, (String) data[i]), data[i+1]))
      return false;
  return true;
}


static String hfulltag(String tag) {
  return hfulltag(tag, "");
}

static String hfulltag(String tag, Object contents, Object... params) {
  return hopeningTag(tag, params) + str(contents) + "</" + tag + ">";
}


static String fulltag(String tag) {
  return hfulltag(tag);
}



static String fulltag(String tag, Object contents, Object... params) {
  return hfulltag(tag, contents, params);
}


static String joinNempties(String sep, Object... strings) {
  return joinStrings(sep, strings);
}

static String joinNempties(String sep, Iterable strings) {
  return joinStrings(sep, strings);
}


static String joinNemptiesWithComma(Object... strings) {
  return joinNempties(", ", strings);
}

static String joinNemptiesWithComma(Iterable strings) {
  return joinNempties(", ", strings);
}


static List flattenCollectionsAndArrays(Iterable a) {
  List l = new ArrayList();
  for (Object x : a)
    if (x instanceof Collection)
      l.addAll(flattenCollectionsAndArrays((Collection) x));
    else if (x instanceof Object[])
      l.addAll(flattenCollectionsAndArrays(asList((Object[]) x)));
    else
      l.add(x);
  return l;
}

static List flattenCollectionsAndArrays(Object... whatever) {
  return flattenCollectionsAndArrays(ll(whatever));
}


static byte clampToUByte(long l) {
  return (byte) clamp(l, 0, 255);
}


static int zeroToOneToZeroTo255(double brightness) {
  return iround(brightness*255.0);
}


static <A, B> B mapGet(Map<A, B> map, A a) {
  return map == null || a == null ? null : map.get(a);
}

static <A, B> B mapGet(A a, Map<A, B> map) {
  return map == null || a == null ? null : map.get(a);
}


// undefined color, seems to be all black in practice
static BufferedImage newGrayBufferedImage(int w, int h) {
  return new BufferedImage(w, h, BufferedImage.TYPE_BYTE_GRAY);
}

static BufferedImage newGrayBufferedImage(int w, int h, byte[] pixels) {
  return byteArrayToGrayBufferedImage(pixels, w, h);
}


static String joinNemptiesWithSpace(String... strings) {
  return joinNempties(" ", strings);
}

static String joinNemptiesWithSpace(Collection<String> strings) {
  return joinNempties(" ", strings);
}


static List flattenCollections(Iterable a) {
  List l = new ArrayList();
  for (Object x : a)
    if (x instanceof Collection)
      l.addAll(flattenCollections((Collection) x));
    else
      l.add(x);
  return l;
}


static <A> A[] arrayOfType(Class<A> type, int n) {
  return makeArray(type, n);
}

static <A> A[] arrayOfType(int n, Class<A> type) {
  return arrayOfType(type, n);
}


static Object swingCall(final Object o, final String method, final Object... args) {
  return swing(new F0<Object>() { public Object get() { try {  return call(o, method, args);  } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "return call(o, method, args);"; }});
}


static String lines(Iterable lines) { return fromLines(lines); }
static String lines(Object[] lines) { return fromLines(asList(lines)); }
static List<String> lines(String s) { return toLines(s); }

// convenience map call
static <A> String lines(Iterable<A> l, IF1<A, String> f) {
  return mapToLines(l, f);
}


static List flattenIterablesAndArrays(Iterable a) {
  List l = new ArrayList();
  for (Object x : a)
    if (x instanceof Iterable)
      l.addAll(flattenIterablesAndArrays((Iterable) x));
    else if (x instanceof Iterator)
      l.addAll(flattenIterablesAndArrays(asList((Iterator) x)));
    else if (x instanceof Object[])
      l.addAll(flattenIterablesAndArrays(asList((Object[]) x)));
    else
      l.add(x);
  return l;
}


static IterableIterator<Integer> countIterator(int b) { return countIterator(0, b); }
static IterableIterator<Integer> countIterator(int a, int b) {
  return countIterator_exclusive(a, b);
}



static <A> IterableIterator<A> countIterator(int b, IF1<Integer, A> f) { return countIterator(0, b, f); }
static <A> IterableIterator<A> countIterator(int a, int b, IF1<Integer, A> f) {
  return countIterator_exclusive(a, b, f);
}

static IterableIterator<Integer> countIterator(int a, int b, int step) {
  return countIterator_exclusive_step(a, b, step);
}

static <A> IterableIterator<A> countIterator(double a, double b, double step, IF1<Double, A> f) {
  return countIterator_exclusive_step(a, b, step, f);
}

static <A> IterableIterator<Double> countIterator(double a, double b, double step) {
  return countIterator_exclusive_step(a, b, step);
}

static <A> IterableIterator<A> countIterator(IF1<Double, A> f, double a, double b, double step) {
  return countIterator(a, b, step, f);
}

static <A> IterableIterator<A> countIterator(IF1<Integer, A> f, int b) { return countIterator(f, 0, b); }
static <A> IterableIterator<A> countIterator(IF1<Integer, A> f, int a, int b) {
  return countIterator_exclusive(a, b, f);
}

static <A> IterableIterator<Integer> countIterator(List l) {
  return countIterator(l(l));
}



static <A> A safeGet(List<A> l, int i) {
  return i >= 0 && i < l(l) ? l.get(i) : null;
}


static IterableIterator<String> toLines(File f) {
  return linesFromFile(f);
}

static List<String> toLines(String s) {
  List<String> lines = new ArrayList<String>();
  if (s == null) return lines;
  int start = 0;
  while (true) {
    int i = toLines_nextLineBreak(s, start);
    if (i < 0) {
      if (s.length() > start) lines.add(s.substring(start));
      break;
    }

    lines.add(s.substring(start, i));
    if (s.charAt(i) == '\r' && i+1 < s.length() && s.charAt(i+1) == '\n')
      i += 2;
    else
      ++i;

    start = i;
  }
  return lines;
}

static int toLines_nextLineBreak(String s, int start) {
  int n = s.length();
  for (int i = start; i < n; i++) {
    char c = s.charAt(i);
    if (c == '\r' || c == '\n')
      return i;
  }
  return -1;
}


static Runnable _topLevelErrorHandling(Runnable r) {


  if (r == null) return null;
  
  // maybe we don't want this anymore. just dm_current_generic()
  Object info = _threadInfo();
  Object mod = dm_current_generic();
  Runnable r2 = r;
  
  if (info != null || mod == null)
    r2 = new Runnable() {  public void run() { try { 
       AutoCloseable __1 =  (AutoCloseable) (rcall("enter", mod)); try {
      _threadInheritInfo(info);
      r.run();
    
} finally { _close(__1); }} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "temp (AutoCloseable) rcall enter(mod);\r\n      _threadInheritInfo(info);\r\n    ..."; }};
  r2 = rPcall(r2);
  return r2;

}


static String defaultThreadName_name;

static String defaultThreadName() {
  if (defaultThreadName_name == null)
    defaultThreadName_name = "A thread by " + programID();
  return defaultThreadName_name;
}


static Random defaultRandomGenerator() {
  { Random r = customRandomizerForThisThread(); if (r != null) return r; }
  return ThreadLocalRandom.current();
}


static Random getRandomizer(Random r) {
  return r != null ? r : defaultRandomGenerator();
}


static <A> A oneOf(List<A> l) {
  if (empty(l)) return null;
  int n = l.size();
  return n == 1 ? first(l) : l.get(defaultRandomizer().nextInt(n));
}

static char oneOf(String s) {
  return empty(s) ? '?' : s.charAt(random(l(s)));
}

static <A> A oneOf(A... l) {
  return oneOf(asList(l));
}


static <A> A collectionGet(Collection<A> c, int idx) {
  if (c == null || idx < 0 || idx >= l(c)) return null;
  if (c instanceof List) return listGet((List<A>) c, idx);
  Iterator<A> it = c.iterator();
  for (int i = 0; i < idx; i++) if (it.hasNext()) it.next(); else return null;
  return it.hasNext() ? it.next() : null;
}


static <A, B> Pair<A, B> entryToPair(Map.Entry<A, B> e) {
  return mapEntryToPair(e);
}


static <A, B> Set<Map.Entry<A,B>> entries(Map<A, B> map) {
  return _entrySet(map);
}


static <A> List<A> cloneSubList(List<A> l, int startIndex, int endIndex) {
  return newSubList(l, startIndex, endIndex);
}

static <A> List<A> cloneSubList(List<A> l, int startIndex) {
  return newSubList(l, startIndex);
}


static void removeSubList(List l, int from, int to) {
  if (l != null) subList(l, from, to).clear();
}

static void removeSubList(List l, int from) {
  if (l != null) subList(l, from).clear();
}


// from: https://stackoverflow.com/questions/14416107/int-array-to-bufferedimage
// pixels are RGB pixels
static BufferedImageWithMeta intArrayToBufferedImage(int[] pixels, int w) { return intArrayToBufferedImage(pixels, w, pixels.length/w); }
static BufferedImageWithMeta intArrayToBufferedImage(int[] pixels, int w, int h) {
  if (w == 0 || h == 0) return null;
  
  int[] bitMasks = new int[]{0xFF0000, 0xFF00, 0xFF, 0xFF000000};
  SinglePixelPackedSampleModel sm = new SinglePixelPackedSampleModel(DataBuffer.TYPE_INT, w, h, bitMasks);
  DataBufferInt db = new DataBufferInt(pixels, pixels.length);
  WritableRaster wr = Raster.createWritableRaster(sm, db, new Point());
  return new BufferedImageWithMeta(ColorModel.getRGBdefault(), wr, false, null);
}

static BufferedImageWithMeta intArrayToBufferedImage(int w, int... pixels) {
  return intArrayToBufferedImage(pixels, w);
}


// undefined color, seems to be all black in practice
// This is without alpha?
static BufferedImage newBufferedImage(int w, int h) {
  return new BufferedImage(w, h, BufferedImage.TYPE_INT_RGB);
}


static BufferedImage newBufferedImage(int w, int h, RGB rgb) {
  return newBufferedImage(w, h, rgb.getColor());
}


static BufferedImage newBufferedImage(int w, int h, Color color) {
  BufferedImage img = newBufferedImage(w, h);
  Graphics2D g = img.createGraphics();
  g.setColor(or(color, Color.white));
  g.fillRect(0, 0, w, h);
  return img;
}


static BufferedImage newBufferedImage(Pt p, Color color) {
  return newBufferedImage(p.x, p.y, color);
}



static BufferedImage newBufferedImage(WidthAndHeight size, Color color) {
  return newBufferedImage(size.w(), size.h(), color);
}


// This one is with alpha...
static BufferedImage newBufferedImage(int w, int h, int[] pixels) {
  return intArrayToBufferedImage(pixels, w, h);
}


static <A> IterableIterator<A> filterIterator(final Iterator<A> it, final F1<A, Boolean> f) {
  if (it == null) return null;
  return iff(new F0<Object>() { public Object get() { try { 
    while (it.hasNext()) {
      A a = it.next();
      if (callF(f, a))
        return a;
    }
    return endMarker();
   } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "while (it.hasNext()) {\r\n      A a = it.next();\r\n      if (callF(f, a))\r\n     ..."; }});
}

static <A> IterableIterator<A> filterIterator(final Iterator<A> it, final IF1<A, Boolean> f) {
  if (it == null) return null;
  return iff(new F0<Object>() { public Object get() { try { 
    while (it.hasNext()) {
      A a = it.next();
      if (callF(f, a))
        return a;
    }
    return endMarker();
   } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "while (it.hasNext()) {\r\n      A a = it.next();\r\n      if (callF(f, a))\r\n     ..."; }});
}

static <A> IterableIterator<A> filterIterator(final F1<A, Boolean> f, final Iterator<A> it) {
  return filterIterator(it, f);
}

static <A> IterableIterator<A> filterIterator(Collection<A> l, IF1<A, Boolean> f) {
  if (l == null) return null;
  Iterator<A> it = iterator(l);
  return iff(new F0<Object>() { public Object get() { try { 
    while (it.hasNext()) {
      A a = it.next();
      if (f.get(a))
        return a;
    }
    return endMarker();
   } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "while (it.hasNext()) {\r\n      A a = it.next();\r\n      if (f.get(a))\r\n        ..."; }});
}

static <A> IterableIterator<A> filterIterator(IF1<A, Boolean> f, Iterator<A> it) {
  return filterIterator(it, f);
}


static TimerTask timerTask(final Object r, final java.util.Timer timer) {
  return new TimerTask() {
    public void run() {
      
      if (!licensed())
        timer.cancel();
      else
        pcallF(r);
    }
  };
}


static <A> A vmBus_timerStarted(A timer) {
  vmBus_send("timerStarted", timer, costCenter());
  return timer;
}


static long clockToSysTimeDiff() {
  return sysNow()-now();
}




static Boolean grabbableIntPixels_succeeded;
static boolean grabbableIntPixels_enable = true;

static GrabbableIntPixels grabbableIntPixels(BufferedImage img) {
  if (img == null || !grabbableIntPixels_enable) return null;
  try {
    var result = grabbableIntPixels_impl(img);
    grabbableIntPixels_succeeded = result != null;
    return result;
  } catch (Throwable _e) {
    grabbableIntPixels_succeeded = false;
  
throw rethrow(_e); }
}

static GrabbableIntPixels grabbableIntPixels_impl(BufferedImage img) {
  Raster raster = img.getRaster();
  SampleModel _sampleModel = raster.getSampleModel();
  if (!(_sampleModel instanceof SinglePixelPackedSampleModel)) return null;
  SinglePixelPackedSampleModel sampleModel =  (SinglePixelPackedSampleModel) _sampleModel;
  DataBufferInt dataBuffer =  (DataBufferInt) (raster.getDataBuffer());
  assertEquals(1, dataBuffer.getNumBanks());
  assertEquals(DataBuffer.TYPE_INT, dataBuffer.getDataType());

  // Let's at this point assume the raster data is what we
  // think it is... (TODO: test on unusual platforms)
  
  int w = img.getWidth(), h = img.getHeight();
  int scanlineStride = sampleModel.getScanlineStride();
  int[] pixels = dataBuffer.getData();
  int offset = dataBuffer.getOffset();
  int translateX = raster.getSampleModelTranslateX();
  int translateY = raster.getSampleModelTranslateY();
  offset += -translateX-translateY*scanlineStride;
  return new GrabbableIntPixels(pixels, w, h, offset, scanlineStride);
}


static BufferedImage toBufferedImageOpt(Object o) {
  if (o instanceof BufferedImage) return ((BufferedImage) o);
  if (o instanceof Image) return copyImage((Image) o);
  if (o instanceof MakesBufferedImage)
    return ((MakesBufferedImage) o).getBufferedImage();
    
  
      
  String c = getClassName(o);
  
  // Keep this because it also works on imported objects
  if (eqOneOf(c, "main$BWImage", "main$RGBImage"))
    return (BufferedImage) call(o, "getBufferedImage");
 
  
  
  return null;
}


static boolean hasJPEGExtension(File f) {
  return ewicOneOf(fileName(f), ".jpg", ".jpeg");
}


static void saveJPG(BufferedImage img, File file) { try {
  if (!ImageIO.write(img, "jpeg", mkdirsFor(file))) {
    print("Reconstructing image for saving JPEG");
    img = reconstructBufferedImage(img);
    if (!ImageIO.write(img, "jpeg", file))
      throw fail("Couldn't write JPEG: " + file + " (" + img + ")");
  }
  vmBus_send("wroteFile", file);
} catch (Exception __e) { throw rethrow(__e); } }

static void saveJPG(File file, BufferedImage img) { try {
  saveJPG(img, file);
} catch (Exception __e) { throw rethrow(__e); } }


static void savePNG(BufferedImage img, File file) { try {
  File tempFile = new File(file.getPath() + "_temp");
  CriticalAction ca = beginCriticalAction("Save " + f2s(file));
  try {
    ImageIO.write(img, "png", mkdirsFor(tempFile));
    file.delete();
    tempFile.renameTo(file);
  } finally {
    ca.done();
  }
} catch (Exception __e) { throw rethrow(__e); } }

// gotta love convenience & program-smartness
static void savePNG(String file, BufferedImage img) { savePNG(toFile(file), img); }

static void savePNG(File file, BufferedImage img) {
  savePNG(img, file);
}


static void savePNG(File file, RGBImage img) {
  savePNG(file, img.getBufferedImage());
}



static int colorToIntOpaque(Color c) {
  return c.getRGB() | 0xFF000000;
}




static String localDateWithSeconds(long time) {
  SimpleDateFormat format = simpleDateFormat_local("yyyy/MM/dd HH:mm:ss");
  return format.format(time);
}

static String localDateWithSeconds() {
  return localDateWithSeconds(now());
}


static BigInteger bigint(String s) {
  return new BigInteger(s);
}

static BigInteger bigint(long l) {
  return BigInteger.valueOf(l);
}


static Set asSet(Object[] array) {
  HashSet set = new HashSet();
  for (Object o : array)
    if (o != null)
      set.add(o);
  return set;
}

static Set<String> asSet(String[] array) {
  TreeSet<String> set = new TreeSet();
  for (String o : array)
    if (o != null)
      set.add(o);
  return set;
}

static <A> Set<A> asSet(Iterable<A> l) {
  if (l instanceof Set) return (Set) l;
  HashSet<A> set = new HashSet();
  for (A o : unnull(l))
    if (o != null)
      set.add(o);
  return set;
}




static Complex complex(double re, double im) {
  return new Complex(re, im);
}

static Complex complex(double re) {
  return new Complex(re, 0.0);
}

static Complex complex(double[] reIm) {
  if (empty(reIm)) return null;
  if (l(reIm) != 2) throw fail("Need 2 doubles to make complex number");
  return complex(reIm[0], reIm[1]);
}


static Pt addPts(Pt a, Pt b) {
  return a == null ? b : b == null ? a : new Pt(a.x+b.x, a.y+b.y);
}


static String colonCombine(Object... l) {
  return joinNemptiesWithColon(flattenCollectionsAndArrays(ll(l)));
}


static Runnable wrapAsActivity(Object r) {
  if (r == null) return null;
  Runnable r2 = toRunnable(r);


  Object mod = dm_current_generic();
  if (mod == null) return r2;
  return new Runnable() {  public void run() { try { 
    AutoCloseable c =  (AutoCloseable) (rcall("enter", mod));
     AutoCloseable __1 = c; try {
    r2.run();
  
} finally { _close(__1); }} catch (Exception __e) { throw rethrow(__e); } }  public String toString() { return "AutoCloseable c =  (AutoCloseable) (rcall enter(mod));\r\n    temp c;\r\n    r2.r..."; }};

}


static Map<Thread, Boolean> _registerThread_threads;
static Object _onRegisterThread; // voidfunc(Thread)

static Thread _registerThread(Thread t) {
  if (_registerThread_threads == null)
    _registerThread_threads = newWeakHashMap();
  _registerThread_threads.put(t, true);
  vm_generalWeakSubMap("thread2mc").put(t, weakRef(mc()));
  callF(_onRegisterThread, t);
  return t;
}

static void _registerThread() {
  _registerThread(Thread.currentThread());
}


static <A> A liftLast(List<A> l) {
  if (empty(l)) return null;
  int i = l(l)-1;
  A a = l.get(i);
  l.remove(i);
  return a;
}

static <A> List<A> liftLast(int n, List<A> l) {
  int i = l(l)-n;
  List<A> part = cloneSubList(l, i);
  removeSubList(l, i);
  return part;
}




static boolean endsWith(String a, String b) {
  return a != null && a.endsWith(b);
}

static boolean endsWith(String a, char c) {
  return nempty(a) && lastChar(a) == c;
}


  static boolean endsWith(String a, String b, Matches m) {
    if (!endsWith(a, b)) return false;
    m.m = new String[] {dropLast(l(b), a)};
    return true;
  }




static String repeat(char c, int n) {
  n = Math.max(n, 0);
  char[] chars = new char[n];
  for (int i = 0; i < n; i++)
    chars[i] = c;
  return new String(chars);
}

static <A> List<A> repeat(A a, int n) {
  n = Math.max(n, 0);
  List<A> l = new ArrayList(n);
  for (int i = 0; i < n; i++)
    l.add(a);
  return l;
}

static <A> List<A> repeat(int n, A a) {
  return repeat(a, n);
}


static List<PtBuffer> g22_allBorderTraces_withDiagonals(IImageRegion region) {
  RegionBorder_innerPoints_withDiagonals walker = new RegionBorder_innerPoints_withDiagonals(region);
  List<PtBuffer> out = new ArrayList();
  walker.onNewTrace(hole -> out.add(new PtBuffer()));
  walker.onFoundPoint(p -> last(out).add(p));
  walker.run();
  return out;
}


static List<PtBuffer> g22_allBorderTraces(IImageRegion region) {
  RegionBorder_innerPoints_v2 walker = new RegionBorder_innerPoints_v2(region);
  List<PtBuffer> out = new ArrayList();
  walker.onNewTrace(hole -> out.add(new PtBuffer()));
  walker.onFoundPoint(p -> last(out).add(p));
  walker.run();
  return out;
}


static String hopeningTag(String tag, Map params) {
  return hopeningTag(tag, mapToParams(params));
}

static String hopeningTag(String tag, Object... params) {
  StringBuilder buf = new StringBuilder();
  buf.append("<" + tag);
  params = unrollParams(params);
  for (int i = 0; i < l(params); i += 2) {
    String name = (String) get(params, i);
    Object val = get(params, i+1);
    if (nempty(name) && val != null) {
      if (eqOneOf(val, html_valueLessParam(), true))
        buf.append(" " + name);
      else {
        String s = str(val);
        if (!empty(s))
          buf.append(" " + name + "=" + htmlQuote(s));
      }
    }
  }
  buf.append(">");
  return str(buf);
}


static String joinStrings(String sep, Object... strings) {
  return joinStrings(sep, Arrays.asList(strings));
}

static String joinStrings(String sep, Iterable strings) {
  StringBuilder buf = new StringBuilder();
  for (Object o : unnull(strings)) { 
    String s = strOrNull(o);
    if (nempty(s)) {
      if (nempty(buf)) buf.append(sep);
      buf.append(s);
    }
  }
  return str(buf);
}


static BufferedImage byteArrayToGrayBufferedImage(byte[] pixels, int w, int h) {
  PixelInterleavedSampleModel sm = new PixelInterleavedSampleModel(
    DataBuffer.TYPE_BYTE,
    w,
    h,
    1, // pixelStride
    w, // scanlineStride,
    new int[] {0} // bandOffsets
  );
  DataBufferByte db = new DataBufferByte(pixels, pixels.length);
  WritableRaster wr = Raster.createWritableRaster(sm, db, new Point());
  return new BufferedImage(grayColorModel(), wr, false, null);
}


static <A> A[] makeArray(Class<A> type, int n) {
  return (A[]) Array.newInstance(type, n);
}


// usually L<S>
static String fromLines(Iterable lines) {
  StringBuilder buf = new StringBuilder();
  if (lines != null)
    for (Object line : lines)
      buf.append(str(line)).append('\n');
  return buf.toString();
}

static String fromLines(String... lines) {
  return fromLines(asList(lines));
}


static List<String> mapToLines(Map map) {
  List<String> l = new ArrayList();
  for (Object key : keys(map))
    l.add(str(key) + " = " + str(map.get(key)));
  return l;
}

static String mapToLines(Map map, Object f) {
  return lines(map(map, f));
}

static String mapToLines(Object f, Map map) {
  return lines(map(map, f));
}

static String mapToLines(Object f, Iterable l) {
  return lines(map(f, l));
}

static <A> String mapToLines(Iterable<A> l, IF1<A, String> f) {
  return mapToLines((Object) f, l);
}

static <A> String mapToLines(IF1<A, String> f, Iterable<A> l) {
  return mapToLines((Object) f, l);
}

static <A, B> String mapToLines(Map<A, B> map, IF2<A, B, String> f) {
  return lines(map(map, f));
}

static <A> String mapToLines(IF1<A, String> f, A data1, A... moreData) {
  return lines(map(f, data1, moreData));
}


static IterableIterator<Integer> countIterator_exclusive(int b) { return countIterator_exclusive(0, b); }
static IterableIterator<Integer> countIterator_exclusive(int a, int b) {
  return new IterableIterator<Integer>() {
    int i = a;
    
    public boolean hasNext() { return i < b; }
    public Integer next() { return i++; }
  };
}

static <A> IterableIterator<A> countIterator_exclusive(int b, IF1<Integer, A> f) { return countIterator_exclusive(0, b, f); }
static <A> IterableIterator<A> countIterator_exclusive(int a, int b, IF1<Integer, A> f) {
  return mapI_if1(f, countIterator_exclusive(a, b));
}


static IterableIterator<Integer> countIterator_exclusive_step(final int a, final int b, final int step) {
  assertTrue("step > 0", step > 0);
  
  return new IterableIterator<Integer>() {
    int i = a;
    
    public boolean hasNext() { return i < b; }
    public Integer next() { var j = i; i += step; return j; }
  };
}

static IterableIterator<Double> countIterator_exclusive_step(double a, double b, double step) {
  assertTrue("step > 0", step > 0);
  
  return new IterableIterator<Double>() {
    double i = a;
    
    public boolean hasNext() { return i < b; }
    public Double next() { var j = i; i += step; return j; }
  };
}

static <A> IterableIterator<A> countIterator_exclusive_step(double a, double b, double step, IF1<Double, A> f) {
  return mapI_if1(f, countIterator_exclusive_step(a, b, step));
}



static CloseableIterableIterator<String> linesFromFile(File f) { return linesFromFile(f, null); }
static CloseableIterableIterator<String> linesFromFile(File f, IResourceHolder resourceHolder) { try {
  if (!fileExists(f)) return emptyCloseableIterableIterator();
  
  if (ewic(f.getName(), ".gz"))
    return linesFromReader(utf8bufferedReader(newGZIPInputStream(f)), resourceHolder);
  
  return linesFromReader(utf8bufferedReader(f), resourceHolder);
} catch (Exception __e) { throw rethrow(__e); } }

static CloseableIterableIterator<String> linesFromFile(String path) { return linesFromFile(path, null); }
static CloseableIterableIterator<String> linesFromFile(String path, IResourceHolder resourceHolder) {
  return linesFromFile(newFile(path), resourceHolder);
}


static Object dm_current_generic() {
  return getWeakRef(dm_current_generic_tl().get());
}


static Object rcall(String method, Object o, Object... args) {
  return call_withVarargs(o, method, args);
}


static Runnable rPcall(Runnable r) {
  return r == null ? null : () -> { try { r.run(); } catch (Throwable __e) { pcallFail(__e); } };
}


static String programID() {
  return getProgramID();
}

static String programID(Object o) {
  return getProgramID(o);
}


static Random customRandomizerForThisThread() {
  return customRandomizerForThisThread_tl().get();
}


static Random defaultRandomizer() {
  return defaultRandomGenerator();
}


static <A> A listGet(List<A> l, int idx) {
  return l != null && idx >= 0 && idx < l.size() ? l.get(idx) : null;
}


static <A> List<A> newSubList(List<A> l, int startIndex, int endIndex) {
  return cloneList(subList(l, startIndex, endIndex));
}

static <A> List<A> newSubList(List<A> l, int startIndex) {
  return cloneList(subList(l, startIndex));
}


static <A> List<A> subList(List<A> l, int startIndex) {
  return subList(l, startIndex, l(l));
}

static <A> List<A> subList(int startIndex, List<A> l) {
  return subList(l, startIndex);
}

static <A> List<A> subList(int startIndex, int endIndex, List<A> l) {
  return subList(l, startIndex, endIndex);
}

static <A> List<A> subList(List<A> l, int startIndex, int endIndex) {
  if (l == null) return null;
  int n = l(l);
  startIndex = Math.max(0, startIndex);
  endIndex = Math.min(n, endIndex);
  if (startIndex > endIndex) return ll();
  if (startIndex == 0 && endIndex == n) return l;
  
  
    return l.subList(startIndex, endIndex);
  
}




static Object costCenter() { return mc(); }


static <A> A assertEquals(Object x, A y) {
  return assertEquals("", x, y);
}

static <A> A assertEquals(String msg, Object x, A y) {
  if (assertVerbose()) return assertEqualsVerbose(msg, x, y);
  if (!(x == null ? y == null : x.equals(y)))
    throw fail((msg != null ? msg + ": " : "") + y + " != " + x);
  return y;
}


  static void assertEquals(Scorer scorer, Object x, Object y) {
    assertEquals(scorer, "", x, y);
  }
  
  static void assertEquals(Scorer scorer, String msg, Object x, Object y) {
    if (scorer == null) { assertEquals(msg, x, y); return; }
    scorer.add(eq(x, y), nullIfEmpty(msg));
  }



// this copies to RGBA
static BufferedImage copyImage(Image img) {
  if (img == null) return null;
  if (img instanceof BufferedImage)
    return copyImage((BufferedImage) img);
  int w = img.getWidth(null), h = img.getHeight(null);
  BufferedImage bi = newBufferedImage(w, h);
  drawImage(bi, img);
  return bi;
}

// this one stays in color model. inconsistent i guess
static BufferedImage copyImage(BufferedImage bi) {
  if (bi == null) return null;
  ColorModel cm = bi.getColorModel();
  boolean isAlphaPremultiplied = cm.isAlphaPremultiplied();
  WritableRaster raster = bi.copyData(bi.getRaster().createCompatibleWritableRaster());
  return new BufferedImage(cm, raster, isAlphaPremultiplied, null);
}


static String fileName(File f) {
  return f == null ? null : f.getName();
}


public static File mkdirsFor(File file) {
  return mkdirsForFile(file);
}



static BufferedImage reconstructBufferedImage(BufferedImage img) {
  if (img == null) return null;
  RGBImage rgb = new RGBImage(img);
  rgb.uncacheBufferedImage();
  return rgb.getBufferedImage();
}


static List<CriticalAction> beginCriticalAction_inFlight = synchroList();

static class CriticalAction implements AutoCloseable {
  String description;
  
  CriticalAction() {}
  CriticalAction(String description) {
  this.description = description;}
  
  final public void close(){ done(); }
public void done() {
    beginCriticalAction_inFlight.remove(this);
  }
}

static CriticalAction beginCriticalAction(String description) {
  ping();
  CriticalAction c = new CriticalAction(description);
  beginCriticalAction_inFlight.add(c);
  return c;
}

static void cleanMeUp_beginCriticalAction() {
  int n = 0;
  while (nempty(beginCriticalAction_inFlight)) {
    int m = l(beginCriticalAction_inFlight);
    if (m != n) {
      n = m;
      try {
        print("Waiting for " + n2(n, "critical actions") + ": " + join(", ", collect(beginCriticalAction_inFlight, "description")));
      } catch (Throwable __e) { pcallFail(__e); }
    }
    sleepInCleanUp(10);
  }
}


static String f2s(File f) {
  return f == null ? null : f.getAbsolutePath();
}

static String f2s(String s) { return f2s(newFile(s)); }


 static String f2s(java.nio.file.Path p) {
  return p == null ? null : f2s(p.toFile());
}



static File toFile(Object o) {
  if (o instanceof File) return (File) o;
  if (o instanceof String) return new File((String) o);
  throw fail("Not a file: " + o);
}




static SimpleDateFormat simpleDateFormat_local(String format) {
  SimpleDateFormat sdf = new SimpleDateFormat(format);
  sdf.setTimeZone(localTimeZone());
  return sdf;
}


static Map vm_generalWeakSubMap(Object name) {
  synchronized(vm_generalMap()) {
    Map map =  (Map) (vm_generalMap_get(name));
    if (map == null)
      vm_generalMap_put(name, map = newWeakMap());
    return map;
  }
}



static <A> WeakReference<A> weakRef(A a) {
  return newWeakReference(a);
}




static char lastChar(String s) {
  return empty(s) ? '\0' : s.charAt(l(s)-1);
}


static <A> A[] dropLast(A[] a) { return dropLast(a, 1); }
static <A> A[] dropLast(A[] a, int n) {
  if (a == null) return null;
  n = Math.min(n, a.length);
  A[] b = arrayOfSameType(a, a.length-n);
  System.arraycopy(a, 0, b, 0, b.length);
  return b;
}

static <A> List<A> dropLast(List<A> l) {
  return subList(l, 0, l(l)-1);
}

static <A> List<A> dropLast(int n, List<A> l) {
  return subList(l, 0, l(l)-n);
}

static <A> List<A> dropLast(Iterable<A> l) {
  return dropLast(asList(l));
}

static String dropLast(String s) {
  return substring(s, 0, l(s)-1);
}

static String dropLast(String s, int n) {
  return substring(s, 0, l(s)-n);
}

static String dropLast(int n, String s) {
  return dropLast(s, n);
}



static Object[] mapToParams(Map map) {
  return mapToObjectArray(map);
}


static Object[] unrollParams(Object[] params) {
  if (l(params) == 1 && params[0] instanceof Map)
    return mapToParams((Map) params[0]);
  return params;
}


static Object html_valueLessParam_cache;
static Object html_valueLessParam() { if (html_valueLessParam_cache == null) html_valueLessParam_cache = html_valueLessParam_load(); return html_valueLessParam_cache;}

static Object html_valueLessParam_load() {
  return new Object();
}


static String htmlQuote(String s) {
  return "\"" + htmlencode_forParams(s) + "\"";
}


static ColorModel grayColorModel_cache;
static ColorModel grayColorModel() { if (grayColorModel_cache == null) grayColorModel_cache = grayColorModel_load(); return grayColorModel_cache;}

static ColorModel grayColorModel_load() {
  return newGrayBufferedImage(1, 1).getColorModel();
}


static boolean fileExists(String path) {
  return path != null && new File(path).exists();
}

static boolean fileExists(File f) {
  return f != null && f.exists();
}


static CloseableIterableIterator emptyCloseableIterableIterator_instance = new CloseableIterableIterator() {
  public Object next() { throw fail(); }
  public boolean hasNext() { return false; }
};

static <A> CloseableIterableIterator<A> emptyCloseableIterableIterator() {
  return emptyCloseableIterableIterator_instance; 
}


static CloseableIterableIterator<String> linesFromReader(Reader r) { return linesFromReader(r, null); }
static CloseableIterableIterator<String> linesFromReader(Reader r, IResourceHolder resourceHolder) {
  final BufferedReader br = bufferedReader(r);
  return holdResource(resourceHolder, iteratorFromFunction_f0_autoCloseable(new F0<String>() { public String get() { try {  return readLineFromReaderWithClose(br);  } catch (Exception __e) { throw rethrow(__e); } }
  public String toString() { return "return readLineFromReaderWithClose(br);"; }}, _wrapIOCloseable(r)));
}


static BufferedReader utf8bufferedReader(InputStream in) { try {
  return in == null ? null : bufferedReader(_registerIOWrap(new InputStreamReader(in, "UTF-8"), in));
} catch (Exception __e) { throw rethrow(__e); } }

static BufferedReader utf8bufferedReader(File f) { try {
  return utf8bufferedReader(newFileInputStream(f));
} catch (Exception __e) { throw rethrow(__e); } }


static GZIPInputStream newGZIPInputStream(File f) {
  return gzInputStream(f);
}

static GZIPInputStream newGZIPInputStream(InputStream in) {
  return gzInputStream(in);
}


static File newFile(File base, String... names) {
  for (String name : names) base = new File(base, name);
  return base;
}

static File newFile(String name) {
  return name == null ? null : new File(name);
}

static File newFile(String base, String... names) {
  return newFile(newFile(base), names);
}


static <A> A getWeakRef(Reference<A> ref) {
  return ref == null ? null : ref.get();
}


static x30_pkg.x30_util.BetterThreadLocal<WeakReference> dm_current_generic_tl;

static x30_pkg.x30_util.BetterThreadLocal<WeakReference> dm_current_generic_tl() {
  if (dm_current_generic_tl == null)
    dm_current_generic_tl = vm_generalMap_getOrCreate("currentModule", () -> new x30_pkg.x30_util.BetterThreadLocal());
  return dm_current_generic_tl;
}



static String programID;
static String getProgramID() {
  return nempty(programID) ? formatSnippetIDOpt(programID) : "?";
}


// TODO: ask JavaX instead
static String getProgramID(Class c) {
  String id = (String) getOpt(c, "programID");
  if (nempty(id))
    return formatSnippetID(id);
  return "?";
}


static String getProgramID(Object o) {
  return getProgramID(getMainClass(o));
}


static ThreadLocal<Random> customRandomizerForThisThread_tl = new ThreadLocal();

static ThreadLocal<Random> customRandomizerForThisThread_tl() {
  return customRandomizerForThisThread_tl;
}


static ThreadLocal<Boolean> assertVerbose_value = new ThreadLocal();

static void assertVerbose(boolean b) {
  assertVerbose_value.set(b);
}

static boolean assertVerbose() { return isTrue(assertVerbose_value.get()); }


static <A> A assertEqualsVerbose(Object x, A y) {
  assertEqualsVerbose((String) null, x, y);
  return y;
}

// x = expected, y = actual
static <A> A assertEqualsVerbose(String msg, Object x, A y) {
  if (!eq(x, y)) {
    

    throw fail((nempty(msg) ? msg + ": " : "") + "expected: "+ x + ", got: " + y);
  } else
    print("OK" + (empty(msg) ? "" : " " + msg) + ": " + /*sfu*/(x));
  return y;
}


static void assertEqualsVerbose(Scorer scorer, Object x, Object y) { assertEqualsVerbose(scorer, "", x, y); }
static void assertEqualsVerbose(Scorer scorer, String msg, Object x, Object y) {
  if (scorer == null) { assertEqualsVerbose(x, y); return; }
  if (!eq(x, y)) {
    print(appendColonIfNempty(msg) + y + " != " + x);
    scorer.add(false);
  } else {
    print("OK: " + appendColonIfNempty(msg) + x);
    scorer.add(true);
  }
}



static String nullIfEmpty(String s) {
  return isEmpty(s) ? null : s;
}

static <A, B> Map<A, B> nullIfEmpty(Map<A, B> map) {
  return isEmpty(map) ? null : map;
}

static <A> List<A> nullIfEmpty(List<A> l) {
  return isEmpty(l) ? null : l;
}


// changes & returns canvas
static BufferedImage drawImage(BufferedImage canvas, Image img, Pt p) {
  return drawImageOnImage(img, canvas, p.x, p.y);
}

static void drawImage(BufferedImage g, Image img) { drawImage(graphics(g), img); }

static void drawImage(Graphics2D g, Image img) {
  drawImage(g, img, 0, 0);
}

static void drawImage(Graphics2D g, Image img, Pt p) {
  drawImage(g, img, p.x, p.y);
}

static void drawImage(Graphics2D g, Image img, int x, int y) {
  { if (g != null) g.drawImage(img, x, y, null); }
}


public static File mkdirsForFile(File file) {
  File dir = file.getParentFile();
  if (dir != null) { // is null if file is in current dir
    dir.mkdirs();
    if (!dir.isDirectory())
      if (dir.isFile()) throw fail("Please delete the file " + f2s(dir) + " - it is supposed to be a directory!");
      else throw fail("Unknown IO exception during mkdirs of " + f2s(file));
  }
  return file;
}

public static String mkdirsForFile(String path) {
  mkdirsForFile(new File(path));
  return path;
}


static int done_minPrint = 10;

static long done(long startTime, String desc) {
  long time = now()-startTime;
  if (time >= done_minPrint)
    print(desc + " [" + time + " ms]");
  return time;
}

static long done(String desc, long startTime) {
  return done(startTime, desc);
}

static long done(long startTime) {
  return done(startTime, "");
}


static List collect(Iterable c, String field) {
  return collectField(c, field);
}

static List collect(String field, Iterable c) {
  return collectField(c, field);
}

/*ifclass Concept
static L collect(Class c, S field) {
  ret collect(list(c), field);
}
endif
TODO: make translator ignore stuff in ifclass until resolved
*/


static void sleepInCleanUp(long ms) { try {
  if (ms < 0) return;
  Thread.sleep(ms);
} catch (Exception __e) { throw rethrow(__e); } }


static TimeZone localTimeZone() {
  return getTimeZone(standardTimeZone());
  // TimeZone.getDefault()?
}


static <A, B> Map<A, B> newWeakMap() {
  return newWeakHashMap();
}


static <A> WeakReference<A> newWeakReference(A a) {
  return a == null ? null : new WeakReference(a);
}




static <A> A[] arrayOfSameType(A[] a, int n) {
  return newObjectArrayOfSameType(a, n);
}


static Object[] mapToObjectArray(Map map) {
  List l = new ArrayList();
  for (Object o : keys(map)) {
    l.add(o);
    l.add(map.get(o));
  }
  return toObjectArray(l);
}

static Object[] mapToObjectArray(Object f, Collection l) {
  int n = l(l);
  Object[] array = new Object[n];
  if (n != 0) {
    Iterator it = iterator(l);
    for (int i = 0; i < n; i++)
      array[i] = callF(f, it.next());
  }
  return array;
}

static Object[] mapToObjectArray(Object f, Object[] l) {
  int n = l(l);
  Object[] array = new Object[n];
  for (int i = 0; i < n; i++)
    array[i] = callF(f, l[i]);
  return array;
}

static <A> Object[] mapToObjectArray(Collection<A> l, IF1<A, Object> f) {
  return mapToObjectArray(f, l);
}

static <A> Object[] mapToObjectArray(A[] l, IF1<A, Object> f) {
  return mapToObjectArray(f, l);
}

static <A> Object[] mapToObjectArray(IF1<A, Object> f, A[] l) {
  int n = l(l);
  Object[] array = new Object[n];
  for (int i = 0; i < n; i++)
    array[i] = f.get(l[i]);
  return array;
}

static <A> Object[] mapToObjectArray(IF1<A, Object> f, Collection<A> l) {
  int n = l(l);
  Object[] array = new Object[n];
  if (n != 0) {
    Iterator it = iterator(l);
    for (int i = 0; i < n; i++)
      array[i] = callF(f, it.next());
  }
  return array;
}


// this should be on by default now I think, but it may break
// legacy code...
static ThreadLocal<Boolean> htmlencode_forParams_useV2 = new ThreadLocal();

static String htmlencode_forParams(String s) {
  if (s == null) return "";
  if (isTrue(htmlencode_forParams_useV2.get()))
    return htmlencode_forParams_v2(s);
    
  StringBuilder out = new StringBuilder(Math.max(16, s.length()));
  for (int i = 0; i < s.length(); i++) {
      char c = s.charAt(i);
      if (c > 127 || c == '"' || c == '<' || c == '>') {
          out.append("&#");
          out.append((int) c);
          out.append(';');
      } else
          out.append(c);
  }
  return out.toString();
}


static BufferedReader bufferedReader(Reader r) { return bufferedReader(r, 8192); }
static BufferedReader bufferedReader(Reader r, int bufSize) {
  if (r == null) return null;
  return r instanceof BufferedReader ? (BufferedReader) r : _registerIOWrap(new BufferedReader(r, bufSize), r);
}

static BufferedReader bufferedReader(File f) {
  return utf8bufferedReader(f);
}


static <A extends AutoCloseable> A holdResource(IResourceHolder holder, A a) {
  { if (holder != null) holder.add(a); }
  return a;
}


static <A> CloseableIterableIterator<A> iteratorFromFunction_f0_autoCloseable(final F0<A> f, final AutoCloseable closeable) {
  class IFF2 extends CloseableIterableIterator<A> {
    A a;
    boolean done = false;
    
    public boolean hasNext() {
      getNext();
      return !done;
    }
    
    public A next() {
      getNext();
      if (done) throw fail();
      A _a = a;
      a = null;
      return _a;
    }
    
    void getNext() {
      if (done || a != null) return;
      a = f.get();
      done = a == null;
    }
    
    public void close() throws Exception {
      if (closeable != null) closeable.close();
    }
  };
  return new IFF2();
}


static String readLineFromReaderWithClose(BufferedReader r) { try {
  String s = r.readLine();
  if (s == null) r.close();
  return s;
} catch (Exception __e) { throw rethrow(__e); } }


static AutoCloseable _wrapIOCloseable(final AutoCloseable c) {
  return c == null ? null : new AutoCloseable() { public String toString() { return "c.close();\r\n    _registerIO(c, null, false);"; } public void close() throws Exception { c.close();
    _registerIO(c, null, false);
  }};
}



static <A> A _registerIOWrap(A wrapper, Object wrapped) {
  return wrapper;
}


static FileInputStream newFileInputStream(File path) throws IOException {
  return newFileInputStream(path.getPath());
}

static FileInputStream newFileInputStream(String path) throws IOException {
  FileInputStream f = new FileInputStream(path);
  _registerIO(f, path, true);
  return f;
}


static int gzInputStream_defaultBufferSize = 65536;

static GZIPInputStream gzInputStream(File f) { try {
  return gzInputStream(new FileInputStream(f));
} catch (Exception __e) { throw rethrow(__e); } }

static GZIPInputStream gzInputStream(File f, int bufferSize) { try {
  return gzInputStream(new FileInputStream(f), bufferSize);
} catch (Exception __e) { throw rethrow(__e); } }

static GZIPInputStream gzInputStream(InputStream in) {
  return gzInputStream(in, gzInputStream_defaultBufferSize);
}

static GZIPInputStream gzInputStream(InputStream in, int bufferSize) { try {
  return _registerIOWrap(new GZIPInputStream(in, gzInputStream_defaultBufferSize), in);
} catch (Exception __e) { throw rethrow(__e); } }


static String formatSnippetIDOpt(String s) {
  return isSnippetID(s) ? formatSnippetID(s) : s;
}


static String formatSnippetID(String id) {
  return "#" + parseSnippetID(id);
}

static String formatSnippetID(long id) {
  return "#" + id;
}


static String appendColonIfNempty(String s) {
  return empty(s) ? "" : s + ": ";
}


static boolean isEmpty(Collection c) {
  return c == null || c.isEmpty();
}

static boolean isEmpty(File f) {
  return f == null || f.length() == 0;
}

static boolean isEmpty(CharSequence s) {
  return s == null || s.length() == 0;
}

static boolean isEmpty(Object[] a) { return a == null || a.length == 0; }
static boolean isEmpty(byte[] a) { return a == null || a.length == 0; }

static boolean isEmpty(Map map) {
  return map == null || map.isEmpty();
}




static boolean isEmpty(AppendableChain c) { return c == null; }


static boolean isEmpty(IntSize l) { return l == null || l.size() == 0; }


// changes & returns canvas
static BufferedImage drawImageOnImage(Image img, BufferedImage canvas, int x, int y) {
  createGraphics(canvas).drawImage(img, x, y, null);
  return canvas;
}

static BufferedImage drawImageOnImage(Image img, BufferedImage canvas) {
  return drawImageOnImage(img, canvas, 0, 0);
}





static Graphics2D graphics(BufferedImage img) {
  return imageGraphics(img);
}


static List collectField(Iterable c, String field) {
  List l = new ArrayList();
  if (c != null) for (Object a : c)
    l.add(getOpt(a, field));
  return l;
}

static List collectField(String field, Iterable c) {
  return collectField(c, field);
}




static TimeZone getTimeZone(String name) {
  return TimeZone.getTimeZone(name);
}


static String standardTimeZone_name = "Europe/Berlin";

static String standardTimeZone() {
  return standardTimeZone_name;
}




static <A> A[] newObjectArrayOfSameType(A[] a) { return newObjectArrayOfSameType(a, a.length); }
static <A> A[] newObjectArrayOfSameType(A[] a, int n) {
  return (A[]) Array.newInstance(a.getClass().getComponentType(), n);
}


static String htmlencode_forParams_v2(String s) {
  if (s == null) return "";
  StringBuilder out = new StringBuilder(Math.max(16, s.length()));
  for (int i = 0; i < s.length(); i++) {
      char c = s.charAt(i);
      if (c > 127 || c == '"' || c == '<' || c == '>' || c == '&') {
          out.append("&#");
          out.append((int) c);
          out.append(';');
      } else
          out.append(c);
  }
  return out.toString();
}


static void _registerIO(Object object, String path, boolean opened) {
}


  public static boolean isSnippetID(String s) {
    try {
      parseSnippetID(s);
      return true;
    } catch (RuntimeException e) {
      return false;
    }
  }


public static long parseSnippetID(String snippetID) {
  long id = Long.parseLong(shortenSnippetID(snippetID));
  if (id == 0) throw fail("0 is not a snippet ID");
  return id;
}


static Map<BufferedImage, Object> createGraphics_modulators = synchroIdentityHashMap();

static Graphics2D createGraphics(BufferedImage img) {
  Graphics2D g = img.createGraphics();
  Object mod = createGraphics_modulators.get(img);
  if (mod != null)
    callF(mod, g);
  return g;
}

// mod: voidfunc(Graphics2D)
static void createGraphics_modulate(BufferedImage img, Object mod) {
  mapPut2(createGraphics_modulators, img, mod);
}


static ThreadLocal<Boolean> imageGraphics_antiAlias = new ThreadLocal();

static Graphics2D imageGraphics(BufferedImage img) {
  return !isFalse(imageGraphics_antiAlias.get()) ? antiAliasGraphics(img) : createGraphics(img);
}




static String shortenSnippetID(String snippetID) {
  if (snippetID.startsWith("#"))
    snippetID = snippetID.substring(1);
  String httpBlaBla = "http://tinybrain.de/";
  if (snippetID.startsWith(httpBlaBla))
    snippetID = snippetID.substring(httpBlaBla.length());
  return "" + parseLong(snippetID);
}


static <A, B> Map<A, B> synchroIdentityHashMap() {
  return synchroMap(new IdentityHashMap());
}


static <A, B> void mapPut2(Map<A, B> map, A key, B value) {
  if (map != null && key != null)
    if (value != null) map.put(key, value);
    else map.remove(key);
}


static Graphics2D antiAliasGraphics(BufferedImage img) {
  return antiAliasOn(createGraphics(img));
}




static long parseLong(String s) {
  if (empty(s)) return 0;
  return Long.parseLong(dropSuffix("L", s));
}

static long parseLong(Object s) {
  return Long.parseLong((String) s);
}


static Graphics2D antiAliasOn(Graphics2D g) {
  g.setRenderingHint(RenderingHints.KEY_TEXT_ANTIALIASING, RenderingHints.VALUE_TEXT_ANTIALIAS_ON);
  g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
  return g;
}




static String dropSuffix(String suffix, String s) {
  return nempty(suffix) && endsWith(s, suffix) ? s.substring(0, l(s)-l(suffix)) : s;
}




static interface IResourceHolder {
  <A extends AutoCloseable> A add(A a);
  Collection<AutoCloseable> takeAll();
}
static class Chain<A> implements Iterable<A> {
  A element;
  Chain<A> next;
  int size;
  
  Chain() {}
  Chain(A element) {
  this.element = element; size = 1; }
  Chain(A element, Chain<A> next) {
  this.next = next;
  this.element = element;
    size = next != null ? next.size+1 : 1;
  }
  
  public String toString() { return str(toList()); }
  
  ArrayList<A> toList() {
    ArrayList<A> l = emptyList(size);
    Chain<A> c = this;
    while (c != null) {
      l.add(c.element);
      c = c.next;
    }
    return l;
  }
  
  // TODO: optimize
  public Iterator<A> iterator() { return toList().iterator(); }
}
// both the outer outline and the outline of a hole are called a "trace"
// should return outer outline first and then outline of holes

// seems to return first point again at the end sometimes

static class RegionBorder_innerPoints_v2 extends AbstractBorderTracer implements IFieldsToList{
  IImageRegion region;
  RegionBorder_innerPoints_v2() {}
  RegionBorder_innerPoints_v2(IImageRegion region) {
  this.region = region;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + region + ")"; }public Object[] _fieldsToList() { return new Object[] {region}; }

  Rect bounds; // region bounds
  int x, y, dir;
  Iterator<Pt> it;
  byte[] reachedInDirections; // bits 0 to 3
  boolean tracing = false;
  int nTrace; // 1 for outline, 2+ for hole

  // directions (0 = right, 1 = down, 2 = left, 3 = up)
  static Pt[] directions = {
    pt(1, 0), pt(0, 1), pt(-1, 0), pt(0, -1) // r, d, l, u
  };
  
  void init() {
    bounds = region.bounds();
    reachedInDirections = new byte[area(bounds)];
    it = region.pixelIterator();
  }

  public boolean step() {
    if (reachedInDirections == null) init();
    
    if (tracing)
      return walkOnePixel();
    else
      return findFirstPixel();
  }
  
  boolean walkOnePixel() {
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    if ((reachedInDirections[posInBounds] & (1 << dir)) != 0) {
      traceDone();
      tracing = false;
      return includeHoles;
    }
    
    reachedInDirections[posInBounds] |= (byte) 1 << dir;
    foundPoint(x, y);
      
    for (int turn = 3; turn <= 6; turn++) { // try left, straight, right, back
      int newDir = (dir+turn) & 3;
      Pt d = directions[newDir];
      int x2 = x+d.x, y2 = y+d.y;
      boolean b = region.contains(x2, y2);
      
      if (b) {
        x = x2; y = y2; dir = newDir;
        return true;
      }
    }
    
    return true; // no black pixels found in any direction - region must be a single pixel
  }
    
  boolean findFirstPixel() {
    // search for first border pixel
    
    if (!it.hasNext()) return false; // done
    Pt p = it.next();
    x = p.x; y = p.y;
      
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    if (reachedInDirections[posInBounds] != 0) return true; // seen pixel before
    
    // if pixel above is empty, walk to the right
    if (!region.contains(x, y-1))
      { startTrace(0); return true; }
      
    // if pixel on the left is empty, walk upwards
    if (!region.contains(x-1, y))
      { startTrace(3); return true; }
    
    // if pixel on the right is empty, walk downwards
    if (!region.contains(x+1, y))
      { startTrace(1); return true; }
    
    // if pixel below is empty, walk left
    if (!region.contains(x, y+1))
      { startTrace(2); return true; }
  
    // not a border pixel, continue search
    return true;
  }
  
  void startTrace(int dir) {
    this.dir = dir;
    
    // mark point reached from all directions in next step
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    reachedInDirections[posInBounds] = (byte) (15 & ~(1 << dir));
      
    tracing = true;
    newTrace(++nTrace > 1);
  }
  
  void foundPoint(int x, int y) { foundPoint(pt(x, y)); }
  
  // get all points as list
  
   List<Pt> allPoints_cache;
 List<Pt> allPoints() { if (allPoints_cache == null) allPoints_cache = allPoints_load(); return allPoints_cache;}

 List<Pt> allPoints_load() {
    PtBuffer l = new PtBuffer();
    onFoundPoint(p -> l.add(p));
    run();
    return l;
  }
  
  // get outline as OnePath
  
   OnePath onePath_cache;
 OnePath onePath() { if (onePath_cache == null) onePath_cache = onePath_load(); return onePath_cache;}

 OnePath onePath_load() {
    includeHoles(false);
    return new OnePath(allPoints(), true);
  }
  
  // or as OnePathWithOrigin
  
   OnePathWithOrigin onePathWithOrigin_cache;
 OnePathWithOrigin onePathWithOrigin() { if (onePathWithOrigin_cache == null) onePathWithOrigin_cache = onePathWithOrigin_load(); return onePathWithOrigin_cache;}

 OnePathWithOrigin onePathWithOrigin_load() {
    includeHoles(false);
    return new OnePathWithOrigin(allPoints(), true);
  }

  // for debugging 
  void runAndPrint() {
    onNewTrace(hole -> print(!hole ? "new outline" : "new hole"));
    onTraceDone(() -> print("traceDone"));
    onFoundPoint(p -> print("foundPoint " + p));
    stepMaxWithStats(this, 10000);
  }
  
  boolean tracingHole() { return nTrace > 1; }
}
static class BoundsFinder {
  int x1 = Integer.MAX_VALUE, y1 = Integer.MAX_VALUE, x2 = 0, y2 = 0;
  
  BoundsFinder() {}
  BoundsFinder(int w, int h) { x1 = w; y1 = h; }
  
  final void add(Pt p){ addPt(p); }
void addPt(Pt p) {
    if (p != null) addPt(p.x, p.y);
  }
  
  final void add(int x, int y){ addPt(x, y); }
void addPt(int x, int y) {
    if (x < x1) x1 = x;
    if (x > x2) x2 = x;
    if (y < y1) y1 = y;
    if (y > y2) y2 = y;
  }
  
  Rect get() {
    return rectFromPointsOrNull(x1, y1, x2+1, y2+1);
  }
}
// size:
// 64 bytes for 0 to 1 elements
// 96 bytes for 2 to 4 elements

/*
 * #!
 * Ontopia Engine
 * #-
 * Copyright (C) 2001 - 2013 The Ontopia Project
 * #-
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 * 
 *      http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 * !#
 */

static class CompactHashMap<K, V> extends CompactAbstractMap<K, V> {
  final static int INITIAL_SIZE = 3;
  final static double LOAD_FACTOR = 0.6;

  // This object is used to represent a null KEY (null value are kept as is)
  final static Object nullObject = new Object();
  
  /**
   * When a key is deleted this object is put into the hashtable in
   * its place, so that other entries with the same key (collisions)
   * further down the hashtable are not lost after we delete an object
   * in the collision chain.
   */
  final static Object deletedObject = new Object();
  int elements;
  int freecells;
  Object[] table; // key, value, key, value, ...
  //int modCount;

  CompactHashMap() {
    this(INITIAL_SIZE);
  }

  CompactHashMap(int size) {
    table = new Object[(size==0 ? 1 : size)*2];
    elements = 0;
    freecells = tableSize();
    //modCount = 0;
  }
  
  // TODO: allocate smarter
  CompactHashMap(Map<K, V> map) {
    this(0);
    if (map != null) putAll(map);
  }

  // ===== MAP IMPLEMENTATION =============================================

  /**
   * Returns the number of key/value mappings in this map.
   */
  public synchronized int size() {
    return elements;
  }
  
  /**
   * Returns <tt>true</tt> if this map contains no mappings.
   */
  public synchronized boolean isEmpty() {
    return elements == 0;
  }

  /**
   * Removes all key/value mappings in the map.
   */
  public synchronized void clear() {
    elements = 0;
    for (int ix = 0; ix < tableSize(); ix++) {
      key(ix, null);
      value(ix, null);
    }
    freecells = tableSize();
    //modCount++;
  }
  
  /**
   * Returns <tt>true</tt> if this map contains the specified key.
   */
  public synchronized boolean containsKey(Object k) {
    return key(findKeyIndex(k)) != null;
  }
  
  /**
   * Returns <tt>true</tt> if this map contains the specified value.
   */
  public synchronized boolean containsValue(Object v) {
    if (v == null)
      v = (V)nullObject;

    for (int ix = 0; ix < tableSize(); ix++)
      if (value(ix) != null && value(ix).equals(v))
        return true;

    return false;
  }

  /**
   * Returns a read-only set view of the map's keys.
   */
  public synchronized Set<Entry<K, V>> entrySet() {
    return new EntrySet();
  }

  /**
   * Removes the mapping with key k, if there is one, and returns its
   * value, if there is one, and null if there is none.
   */
  public synchronized V remove(Object k) {
    int index = findKeyIndex(k);

    // we found the right position, now do the removal
    if (key(index) != null) {
      // we found the object

      // same problem here as with put
      V v = value(index);
      key(index, deletedObject);
      value(index, deletedObject);
      //modCount++;
      elements--;
      return v;
    } else
      // we did not find the key
      return null;
  }

  /**
   * Adds the specified mapping to this map, returning the old value for
   * the mapping, if there was one.
   */
  public synchronized V put(K k, V v) {
    if (k == null)
      k = (K)nullObject;

    int hash = k.hashCode();
    int index = (hash & 0x7FFFFFFF) % tableSize();
    int offset = 1;
    int deletedix = -1;
    
    // search for the key (continue while !null and !this key)
    while(key(index) != null &&
          !(key(index).hashCode() == hash &&
            key(index).equals(k))) {

      // if there's a deleted mapping here we can put this mapping here,
      // provided it's not in here somewhere else already
      if (key(index) == deletedObject)
        deletedix = index;
      
      index = ((index + offset) & 0x7FFFFFFF) % tableSize();
      offset = offset*2 + 1;

      if (offset == -1)
        offset = 2;
    }
    
    if (key(index) == null) { // wasn't present already
      if (deletedix != -1) // reusing a deleted cell
        index = deletedix;
      else
        freecells--;

      //modCount++;
      elements++;

      key(index, k);
      value(index, v);
      
      // rehash with increased capacity
      if (1 - (freecells / (double) tableSize()) > LOAD_FACTOR)
        rehash(tableSize()*2 + 1);
      return null;
    } else { // was there already
      //modCount++;
      V oldv = value(index);
      value(index, v);
      return oldv;
    }
  }

  /**
   * INTERNAL: Rehashes the hashmap to a bigger size.
   */
  void rehash(int newCapacity) {
    int oldCapacity = tableSize();
    Object[] newTable = new Object[newCapacity*2];

    for (int ix = 0; ix < oldCapacity; ix++) {
      Object k = key(ix);
      if (k == null || k == deletedObject)
        continue;
      
      int hash = k.hashCode();
      int index = (hash & 0x7FFFFFFF) % newCapacity;
      int offset = 1;

      // search for the key
      while(newTable[index*2] != null) { // no need to test for duplicates
        index = ((index + offset) & 0x7FFFFFFF) % newCapacity;
        offset = offset*2 + 1;

        if (offset == -1)
          offset = 2;
      }

      newTable[index*2] = k;
      newTable[index*2+1] = value(ix);
    }

    table = newTable;
    freecells = tableSize() - elements;
  }

  /**
   * Returns the value for the key k, if there is one, and null if
   * there is none.
   */
  public synchronized V get(Object k) {
    return value(findKeyIndex(k));
  }

  /**
   * Returns a virtual read-only collection containing all the values
   * in the map.
   */
  public synchronized Collection<V> values() {
    return new ValueCollection();
  }

  /**
   * Returns a virtual read-only set of all the keys in the map.
   */
  public synchronized Set<K> keySet() {
    return new KeySet();
  }

  // --- Internal utilities

  final int findKeyIndex(Object k) {
    if (k == null)
      k = nullObject;

    int hash = k.hashCode();
    int index = (hash & 0x7FFFFFFF) % tableSize();
    int offset = 1;

    // search for the key (continue while !null and !this key)
    while(key(index) != null &&
          !(key(index).hashCode() == hash &&
            key(index).equals(k))) {
      index = ((index + offset) & 0x7FFFFFFF) % tableSize();
      offset = offset*2 + 1;

      if (offset == -1)
        offset = 2;
    }
    return index;
  }
  
  // --- Key set

  class KeySet extends AbstractSet<K> {
    public int size() { synchronized(CompactHashMap.this) {
      return elements;
    }}

    public boolean contains(Object k) { synchronized(CompactHashMap.this) {
      return containsKey(k);
    }}

    public Iterator<K> iterator() { synchronized(CompactHashMap.this) {
      return new KeyIterator();
    }}
  }

  class KeyIterator<K> implements Iterator<K> {
    private int ix;
    
    private KeyIterator() {
      synchronized(CompactHashMap.this) {
        // walk up to first value, so that hasNext() and next() return
        // correct results
        for (; ix < tableSize(); ix++)
          if (value(ix) != null && key(ix) != deletedObject)
            break;
      }
    }

    public boolean hasNext() { synchronized(CompactHashMap.this) {
      return ix < tableSize();
    }}

    public void remove() {
      throw new UnsupportedOperationException("Collection is read-only");
    }

    public K next() { synchronized(CompactHashMap.this) {
      if (ix >= tableSize())
        throw new NoSuchElementException();
      K key = (K) key(ix++);
      
      // walk up to next value
      for (; ix < tableSize(); ix++)
        if (key(ix) != null && key(ix) != deletedObject)
          break;
      
      // ix now either points to next key, or outside array (if no next)
      return key;
    }}
  }
  
  // --- Entry set
  
  class EntrySet extends AbstractSet<Map.Entry<K, V>> {
    public int size() { synchronized(CompactHashMap.this) {
      return elements;
    }}

    public boolean contains(Object o) { synchronized(CompactHashMap.this) {
      if (o instanceof Map.Entry) {
        Object key = ((Map.Entry) o).getKey();
        if (!containsKey((Map.Entry) o)) return false;
        return eq(((Map.Entry) o).getValue(), get(key));
      }
      return false;
    }}

    public Iterator<Map.Entry<K, V>> iterator() {
      return new EntryIterator();
    }
  }

  class EntryIterator implements Iterator<Map.Entry<K, V>> {
    private int ix;
    
    private EntryIterator() {
      synchronized(CompactHashMap.this) {
        // walk up to first value, so that hasNext() and next() return
        // correct results
        for (; ix < tableSize(); ix++)
          if (value(ix) != null && key(ix) != deletedObject)
            break;
      }
    }

    public boolean hasNext() { synchronized(CompactHashMap.this) {
      return ix < tableSize();
    }}

    public void remove() {
      throw new UnsupportedOperationException("Collection is read-only");
    }

    public Map.Entry<K, V> next() { synchronized(CompactHashMap.this) {
      if (ix >= tableSize())
        throw new NoSuchElementException();
      K key = key(ix);
      V val = value(ix);
      ++ix;
      
      // walk up to next value
      for (; ix < tableSize(); ix++)
        if (key(ix) != null && key(ix) != deletedObject)
          break;
      
      // ix now either points to next key, or outside array (if no next)
      return simpleMapEntry(key, val);
    }}
  }
  
  // --- Value collection

  class ValueCollection<V> extends AbstractCollection<V> {
    public int size() { synchronized(CompactHashMap.this) {
      return elements;
    }}

    public Iterator<V> iterator() {
      return new ValueIterator();
    }

    public boolean contains(Object v) {
      return containsValue(v);
    }
  }

  class ValueIterator<V> implements Iterator<V> {
    private int ix;
    
    private ValueIterator() {
      synchronized(CompactHashMap.this) {
        // walk up to first value, so that hasNext() and next() return
        // correct results
        for (; ix < table.length/2; ix++)
          if (value(ix) != null && value(ix) != deletedObject)
            break;
      }
    }

    public boolean hasNext() { synchronized(CompactHashMap.this) {
      return ix < tableSize();
    }}

    public void remove() {
      throw new UnsupportedOperationException("Collection is read-only");
    }

    public V next() { synchronized(CompactHashMap.this) {
      if (ix >= tableSize())
        throw new NoSuchElementException();
      V value = (V) value(ix++);
      
      // walk up to next value
      for (; ix < tableSize(); ix++)
        if (value(ix) != null && value(ix) != deletedObject)
          break;
      
      // ix now either points to next value, or outside array (if no next)
      return value;
    }}
  }
  
  K key(int i) { return (K) table[i*2]; }
  void key(int i, Object key) { table[i*2] = key; }
  V value(int i) { return (V) table[i*2+1]; }
  void value(int i, Object value) { table[i*2+1] = value; }
  
  int tableSize() { return table.length/2; }
}
static class BufferedImageWithMeta extends BufferedImage implements IMeta {
  BufferedImageWithMeta(ColorModel cm,
    WritableRaster raster,
    boolean isRasterPremultiplied,
    Hashtable<?,?> properties) {
    super(cm, raster, isRasterPremultiplied, properties);
  }

  
// Meta - a "minimal" approach to adding meta-level to Java objects
// (implementing the interface IMeta)

// We allocate one extra field for each Java object to make it
// reasoning-compatible (reasoning-compatible = extensible with
// fields of any name at runtime).
//
// We couldn't go for 0 extra fields (meta values must be linked
// directly from the object) and there are no half fields in
// Java... so there you go.
//
// Also, if you don't use any meta data, you are probably not
// reasoning about anything. The point of reasoning in JavaX is
// to attach information to objects directly used in the program.

// Possible information contained in the meta field:
//   Origin, destination, security level, sender, cost center,
//   purpose, list of reifications, ...

// So here it is. THE FIELD YOU HAVE BEEN WAITING FOR!

// [We also have IMeta to retrofit foreign classes (rare but
// probably useful).]

//////////////////////
// The "meta" field //
//////////////////////

// Generic meta value of any kind, but the typical case is it's a
// Map with extra field values for the object etc.
// "meta" is volatile to avoid synchronization; but you can also synchronize on
// _tempMetaMutex() which is usually the object itself. Collections
// and maps are exempt from using the collections's monitor as the meta
// mutex because their monitor tends to be held for long operations
// (e.g. cloneList). For those we use a substantially more complex
// algorithm using a weakMap. Probably overkill. I may reconsider.

volatile Object meta;

// The meta field is not transient, thus by default it will be
// persisted like anything else unless you customize your object
// to suppress or modulate this.

// ...and the interface methods

public void _setMeta(Object meta) { this.meta = meta; }
public Object _getMeta() { return meta; }

// MOST functions are implemented in IMeta (default implementations)

// Scaffolding convenience functions

final boolean scaffolding(){ return scaffoldingEnabled(); }
final boolean scaffolded(){ return scaffoldingEnabled(); }
boolean scaffoldingEnabled() { return main.scaffoldingEnabled(this); }
boolean scaffoldingEnabled(Object o) { return main.scaffoldingEnabled(o); }

// Implementing setMetaToString

String toString_base() { return super.toString(); }
public String toString() {
  Object o = metaGet("toString", this);
  if (o instanceof String) return ((String) o);
  if (o instanceof IF1) return str(((IF1) o).get(this));
  return toString_base();
}
}
// a variant of thread where you can get the Runnable target later.
// Also notes its existence on the VM bus.
// We should use this exclusively instead of Thread.

static class BetterThread extends Thread {
  Runnable target;
  
  BetterThread(Runnable target) {
  this.target = target; _created(); }
  BetterThread(Runnable target, String name) { super(name);
  this.target = target; _created(); }
  
  void _created() { vmBus_send("threadCreated", this); }
  
  public void run() { try {
    try {
      vmBus_send("threadStarted", this);
      if (target != null) target.run();
    } finally {
      vmBus_send("threadEnded", this); 
    }
  } catch (Exception __e) { throw rethrow(__e); } }
  
  Runnable getTarget() { return target; }
}
static class Complex implements IFieldsToList{
  static final String _fieldOrder = "re im";
  double re;
  double im;
  Complex() {}
  Complex(double re, double im) {
  this.im = im;
  this.re = re;}

public boolean equals(Object o) {
if (!(o instanceof Complex)) return false;
    Complex __1 =  (Complex) o;
    return re == __1.re && im == __1.im;
}

  public int hashCode() {
    int h = -1679819632;
    h = boostHashCombine(h, _hashCode(re));
    h = boostHashCombine(h, _hashCode(im));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {re, im}; }

  double abs() { return sqrt(re*re+im*im); }
  
  double re() { return re; }
  double im() { return im; }
  
  final double angle(){ return phase(); }
double phase() { return Math.atan2(im, re); }
  double fracAngle() { return fracNonNeg(angle()/twoPi()); } // angle as 0 to 1
  
  public String toString() {
    if (im != 0)
      return re == 0 ? im + "i" : re + plusPrefixUnlessMinus(str(im)) + "i";
    else
      return str(re);
  }
}
static final class WidthAndHeightFinal extends Meta implements WidthAndHeight
   , IFieldsToList{
  static final String _fieldOrder = "width height";
  int width;
  int height;
  WidthAndHeightFinal() {}
  WidthAndHeightFinal(int width, int height) {
  this.height = height;
  this.width = width;}

public boolean equals(Object o) {
if (!(o instanceof WidthAndHeightFinal)) return false;
    WidthAndHeightFinal __0 =  (WidthAndHeightFinal) o;
    return width == __0.width && height == __0.height;
}

  public int hashCode() {
    int h = -1177452162;
    h = boostHashCombine(h, _hashCode(width));
    h = boostHashCombine(h, _hashCode(height));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {width, height}; }

  public int getWidth() { return width; }
  public int getHeight() { return height; }
  
  WidthAndHeightFinal(int wAndH) { this(wAndH, wAndH); }
  
  public String toString() { return n2(width) + "*" + n2(height) + " px"; }
  
  
}
static class GrabbableIntPixels implements IFieldsToList{
  static final String _fieldOrder = "data w h offset scanlineStride";
  int[] data;
  int w;
  int h;
  int offset;
  int scanlineStride;
  GrabbableIntPixels() {}
  GrabbableIntPixels(int[] data, int w, int h, int offset, int scanlineStride) {
  this.scanlineStride = scanlineStride;
  this.offset = offset;
  this.h = h;
  this.w = w;
  this.data = data;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + data + ", " + w + ", " + h + ", " + offset + ", " + scanlineStride + ")"; }

public boolean equals(Object o) {
if (!(o instanceof GrabbableIntPixels)) return false;
    GrabbableIntPixels __1 =  (GrabbableIntPixels) o;
    return eq(data, __1.data) && w == __1.w && h == __1.h && offset == __1.offset && scanlineStride == __1.scanlineStride;
}

  public int hashCode() {
    int h = -1183022196;
    h = boostHashCombine(h, _hashCode(data));
    h = boostHashCombine(h, _hashCode(w));
    h = boostHashCombine(h, _hashCode(h));
    h = boostHashCombine(h, _hashCode(offset));
    h = boostHashCombine(h, _hashCode(scanlineStride));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {data, w, h, offset, scanlineStride}; }

  int[] asPackedArray() {
    if (offset == 0 && data.length == w*h) return data;
    int[] pixels = new int[w*h];
    for (int y = 0; y < h; y++)
      arrayCopy(data, offset+y*scanlineStride, pixels, y*h, w);
    return pixels;
  }
}
static abstract class CloseableIterableIterator<A> extends IterableIterator<A> implements AutoCloseable {
  public void close() throws Exception {}
}
static class PtBuffer extends RandomAccessAbstractList  < Pt > {
  LongBuffer buf = new LongBuffer();
  
  PtBuffer() {}
  PtBuffer(int size) { buf.allocate(size); }
  
  PtBuffer(Iterable<Pt> l) {
    if (l != null) for (Pt p : l) add(p);
  }
  
  public int size() { return buf.size(); }
  
  public Pt get(int i) {
    return longToPt(buf.get(i));
  }
  
  public long getLong(int i) {
    return buf.get(i);
  }
  
  public Pt set(int i, Pt val) {
    Pt old = get(i);
    buf.set(i, ptToLong(val));
    return old;
  }
  
  public boolean add(Pt p) {
    buf.add(ptToLong(p));
    return true;
  }
  
  public void add(int x, int y) {
    buf.add(ptToLong(x, y));
  }
  
  public Pt remove(int i) {
    Pt p = get(i);
    buf.remove(i);
    return p;
  }
  
  public void clear() { buf.clear(); }
}
static class ReverseChain<A> implements Iterable<A> {
  A element;
  ReverseChain<A> prev;
  int size;
  
  ReverseChain() {}
  ReverseChain(ReverseChain<A> prev, A element) {
  this.element = element;
  this.prev = prev;
    if (prev == null) size = 1;
    else {
      prev.check();
      size = prev.size+1;
    }
  }
  
  void check() {
    if (size < 1) throw fail("You called the ReverseChain default constructor. Don't do that");
  }
  
  public String toString() {
    return str(toList());
  }
  
  ArrayList<A> toList() {
    check();
    ArrayList<A> l = emptyList(size);
    for (int i = 0; i < size; i++) l.add(null);
    int i = size;
    ReverseChain<A> c = this;
    while (c != null) {
      l.set(--i, c.element);
      c = c.prev;
    }
    return l;
  }
  
  public Iterator<A> iterator() { return toList().iterator(); }
}
// both the outer outline and the outline of a hole are called a "trace"
// should return outer outline first and then outline of holes

// seems to return first point again at the end sometimes

static class RegionBorder_innerPoints_withDiagonals extends AbstractBorderTracer implements IFieldsToList{
  IImageRegion region;
  RegionBorder_innerPoints_withDiagonals() {}
  RegionBorder_innerPoints_withDiagonals(IImageRegion region) {
  this.region = region;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + region + ")"; }public Object[] _fieldsToList() { return new Object[] {region}; }

  Rect bounds; // region bounds
  int x, y;
  int dir; // current direction (1 to 8)
  Iterator<Pt> it;
  byte[] reachedInDirections; // bits 0 to 7
  boolean tracing = false;
  int nTrace; // 1 for outline, 2+ for hole

  void init() {
    bounds = region.bounds();
    reachedInDirections = new byte[area(bounds)];
    it = region.pixelIterator();
  }

  public boolean step() {
    if (reachedInDirections == null) init();
    
    if (tracing)
      return walkOnePixel();
    else
      return findFirstPixel();
  }
  
  boolean walkOnePixel() {
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    if ((reachedInDirections[posInBounds] & (1 << (dir-1))) != 0) {
      traceDone();
      tracing = false;
      return includeHoles;
    }
    
    reachedInDirections[posInBounds] |= (byte) 1 << (dir-1);
     
    foundPoint(x, y);
      
    // try left, half left, straight, half right, right, back
    for (int turn = -2; turn <= 4; turn++) {
      int newDir = modRange_incl(dir+turn, 1, 8);
      Pt d = onePathDirection(newDir);
      int x2 = x+d.x, y2 = y+d.y;
      boolean b = region.contains(x2, y2);
      if (b) {
         
        x = x2; y = y2; dir = newDir;
        return true;
      }
    }
    
     
    return true; // no black pixels found in any direction - region must be a single pixel
  }
    
  boolean findFirstPixel() {
    // search for first border pixel
    
    if (!it.hasNext()) return false; // done
    Pt p = it.next();
    x = p.x; y = p.y;
      
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    if (reachedInDirections[posInBounds] != 0) return true; // seen pixel before
    
    // if pixel above is empty, walk to the right
    if (!region.contains(x, y-1))
      { startTrace(4); return true; }
      
    // if pixel on the left is empty, walk upwards
    if (!region.contains(x-1, y))
      { startTrace(2); return true; }
    
    // if pixel on the right is empty, walk downwards
    if (!region.contains(x+1, y))
      { startTrace(6); return true; }
    
    // if pixel below is empty, walk left
    if (!region.contains(x, y+1))
      { startTrace(8); return true; }
  
    // not a border pixel, continue search
    return true;
  }
  
  void startTrace(int dir) {
    this.dir = dir;
    
    // mark point reached from all directions in next step
    int posInBounds = (y-bounds.y)*bounds.w+x-bounds.x;
    reachedInDirections[posInBounds] = (byte) ~(1 << (dir-1));
      
    tracing = true;
     
    newTrace(++nTrace > 1);
  }
  
  void foundPoint(int x, int y) { foundPoint(pt(x, y)); }
  
  // get all points as list
  
   List<Pt> allPoints_cache;
 List<Pt> allPoints() { if (allPoints_cache == null) allPoints_cache = allPoints_load(); return allPoints_cache;}

 List<Pt> allPoints_load() {
    PtBuffer l = new PtBuffer();
    onFoundPoint(p -> l.add(p));
    run();
    return l;
  }
  
  // get outline as OnePath
  
   OnePath onePath_cache;
 OnePath onePath() { if (onePath_cache == null) onePath_cache = onePath_load(); return onePath_cache;}

 OnePath onePath_load() {
    includeHoles(false);
    return new OnePath(allPoints(), true);
  }
  
  // or as OnePathWithOrigin
  
   OnePathWithOrigin onePathWithOrigin_cache;
 OnePathWithOrigin onePathWithOrigin() { if (onePathWithOrigin_cache == null) onePathWithOrigin_cache = onePathWithOrigin_load(); return onePathWithOrigin_cache;}

 OnePathWithOrigin onePathWithOrigin_load() {
    includeHoles(false);
    return new OnePathWithOrigin(allPoints(), true);
  }

  // for debugging 
  void runAndPrint() {
    onNewTrace(hole -> print(!hole ? "new outline" : "new hole"));
    onTraceDone(() -> print("traceDone"));
    onFoundPoint(p -> print("foundPoint " + p));
    stepMaxWithStats(this, 10000);
  }
  
  boolean tracingHole() { return nTrace > 1; }
}


static class LongBuffer implements Iterable<Long>, ILongQueue, IntSize {
  long[] data;
  int size;
  
  LongBuffer() {}
  LongBuffer(int size) { if (size != 0) data = new long[size]; }
  LongBuffer(Iterable<Long> l) {
    if (l instanceof Collection) allocate(((Collection) l).size());
    addAll(l);
  }
  
  public void add(long i) {
    if (size >= lLongArray(data)) {
      data = resizeLongArray(data, Math.max(1, toInt(Math.min(maximumSafeArraySize(), lLongArray(data)*2L))));
      if (size >= data.length) throw fail("LongBuffer too large: " + size);
    }
    data[size++] = i;
  }
  
  void allocate(int n) {
    data = resizeLongArray(data, max(n, size()));
  }
  
  void addAll(Iterable<Long> l) {
    if (l != null) for (long i : l) add(i);
  }
  
  long[] toArray() {
    return size == 0 ? null : resizeLongArray(data, size);
  }
  
  List<Long> toList() {
    return longArrayToList(data, 0, size);
  }
  
  List<Long> asVirtualList() {
    return listFromFunction(__47 -> get(__47), size);
  }
  
  void reset() { size = 0; }
  void clear() { reset(); }
  
  public int size() { return size; }
  public boolean isEmpty() { return size == 0; }
  
  long get(int idx) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    return data[idx];
  }
  
  void set(int idx, long value) {
    if (idx >= size) throw fail("Index out of range: " + idx + "/" + size);
    data[idx] = value;
  }
  
  long popLast() {
    if (size == 0) throw fail("empty buffer");
    return data[--size];
  }
  
  long last() { return data[size-1]; }
  long nextToLast() { return data[size-2]; }
  
  public String toString() { return squareBracket(joinWithSpace(toList())); }
  
  public Iterator<Long> iterator() {
    return new IterableIterator<Long>() {
      int i = 0;
      
      public boolean hasNext() { return i < size; }
      public Long next() {
        if (!hasNext()) throw fail("Index out of bounds: " + i);
        return data[i++];
      }
    };
  }
  
  void trimToSize() {
    data = resizeLongArray(data, size);
  }
  
  void remove(int idx) {
    arraycopy(data, idx+1, data, idx, size-1-idx);
    --size;
  }
  
  // don't rely on return value if buffer is empty
  public long poll() { 
    return size == 0 ? -1 : data[--size];
  }
}
abstract static class AbstractBorderTracer extends AbstractSteppable {
   transient Set<IVF1<Boolean>> onNewTrace;
public  AbstractBorderTracer onNewTrace(IVF1<Boolean> f) { onNewTrace = createOrAddToSyncLinkedHashSet(onNewTrace, f); return this; }
public  AbstractBorderTracer removeNewTraceListener(IVF1<Boolean> f) { main.remove(onNewTrace, f); return this; }
public   void newTrace(boolean isHole) {  if (onNewTrace != null) for (var listener : onNewTrace) pcallF_typed(listener, isHole); }
   transient Set<IVF1<Pt>> onFoundPoint;
public  AbstractBorderTracer onFoundPoint(IVF1<Pt> f) { onFoundPoint = createOrAddToSyncLinkedHashSet(onFoundPoint, f); return this; }
public  AbstractBorderTracer removeFoundPointListener(IVF1<Pt> f) { main.remove(onFoundPoint, f); return this; }
public   void foundPoint(Pt p) {  if (onFoundPoint != null) for (var listener : onFoundPoint) pcallF_typed(listener, p); }
   transient Set<Runnable> onTraceDone;
public  AbstractBorderTracer onTraceDone(Runnable r) { onTraceDone = createOrAddToSyncLinkedHashSet(onTraceDone, r); return this; }
public  AbstractBorderTracer removeTraceDoneListener(Runnable r) { main.remove(onTraceDone, r); return this; }
public   void traceDone() {  if (onTraceDone != null) for (var listener : onTraceDone) pcallF_typed(listener); }
  
   final public AbstractBorderTracer setIncludeHoles(boolean includeHoles){ return includeHoles(includeHoles); }
public AbstractBorderTracer includeHoles(boolean includeHoles) { this.includeHoles = includeHoles; return this; }  final public boolean getIncludeHoles(){ return includeHoles(); }
public boolean includeHoles() { return includeHoles; }
 boolean includeHoles = true;
}
abstract static class CompactAbstractMap<K, V> implements Map<K, V> {
  public int size() {
      return entrySet().size();
  }

  public boolean isEmpty() {
      return size() == 0;
  }

  public boolean containsValue(Object value) {
      Iterator<Entry<K, V>> i = entrySet().iterator();
      if (value == null) {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (e.getValue() == null)
                  return true;
          }
      } else {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (value.equals(e.getValue()))
                  return true;
          }
      }
      return false;
  }

  public boolean containsKey(Object key) {
      Iterator<Entry<K, V>> i = entrySet().iterator();
      if (key == null) {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (e.getKey() == null)
                  return true;
          }
      } else {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (key.equals(e.getKey()))
                  return true;
          }
      }
      return false;
  }

  public V get(Object key) {
      Iterator<Entry<K, V>> i = entrySet().iterator();
      if (key == null) {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (e.getKey() == null)
                  return e.getValue();
          }
      } else {
          while (i.hasNext()) {
              Entry<K, V> e = i.next();
              if (key.equals(e.getKey()))
                  return e.getValue();
          }
      }
      return null;
  }

  public V put(K key, V value) {
      throw new UnsupportedOperationException();
  }

  public V remove(Object key) {
      Iterator<Entry<K, V>> i = entrySet().iterator();
      Entry<K, V> correctEntry = null;
      if (key == null) {
          while (correctEntry == null && i.hasNext()) {
              Entry<K, V> e = i.next();
              if (e.getKey() == null)
                  correctEntry = e;
          }
      } else {
          while (correctEntry == null && i.hasNext()) {
              Entry<K, V> e = i.next();
              if (key.equals(e.getKey()))
                  correctEntry = e;
          }
      }

      V oldValue = null;
      if (correctEntry != null) {
          oldValue = correctEntry.getValue();
          i.remove();
      }
      return oldValue;
  }

  public void putAll(Map<? extends K, ? extends V> m) {
      for (Entry<? extends K, ? extends V> e : m.entrySet())
          put(e.getKey(), e.getValue());
  }

  public void clear() {
      entrySet().clear();
  }

  public Set<K> keySet() {
      return new AbstractSet<K>() {
          public Iterator<K> iterator() {
              return new Iterator<K>() {
                  private Iterator<Entry<K, V>> i = entrySet().iterator();

                  public boolean hasNext() {
                      return i.hasNext();
                  }

                  public K next() {
                      return i.next().getKey();
                  }

                  public void remove() {
                      i.remove();
                  }
              };
          }

          public int size() {
              return CompactAbstractMap.this.size();
          }

          public boolean isEmpty() {
              return CompactAbstractMap.this.isEmpty();
          }

          public void clear() {
              CompactAbstractMap.this.clear();
          }

          public boolean contains(Object k) {
              return CompactAbstractMap.this.containsKey(k);
          }
      };
  }

  public Collection<V> values() {
      return new AbstractCollection<V>() {
          public Iterator<V> iterator() {
              return new Iterator<V>() {
                  private Iterator<Entry<K, V>> i = entrySet().iterator();

                  public boolean hasNext() {
                      return i.hasNext();
                  }

                  public V next() {
                      return i.next().getValue();
                  }

                  public void remove() {
                      i.remove();
                  }
              };
          }

          public int size() {
              return CompactAbstractMap.this.size();
          }

          public boolean isEmpty() {
              return CompactAbstractMap.this.isEmpty();
          }

          public void clear() {
              CompactAbstractMap.this.clear();
          }

          public boolean contains(Object v) {
              return CompactAbstractMap.this.containsValue(v);
          }
      };
  }

  public abstract Set<Entry<K, V>> entrySet();

  public boolean equals(Object o) {
      if (o == this)
          return true;

      if (!(o instanceof Map))
          return false;
      Map<?, ?> m = (Map<?, ?>) o;
      if (m.size() != size())
          return false;

      try {
          for (Entry<K, V> e : entrySet()) {
              K key = e.getKey();
              V value = e.getValue();
              if (value == null) {
                  if (!(m.get(key) == null && m.containsKey(key)))
                      return false;
              } else {
                  if (!value.equals(m.get(key)))
                      return false;
              }
          }
      } catch (ClassCastException unused) {
          return false;
      } catch (NullPointerException unused) {
          return false;
      }

      return true;
  }

  public int hashCode() {
      int h = 0;
      for (Entry<K, V> entry : entrySet())
          h += entry.hashCode();
      return h;
  }

  public String toString() {
      Iterator<Entry<K, V>> i = entrySet().iterator();
      if (!i.hasNext())
          return "{}";

      StringBuilder sb = new StringBuilder();
      sb.append('{');
      for (; ; ) {
          Entry<K, V> e = i.next();
          K key = e.getKey();
          V value = e.getValue();
          sb.append(key == this ? "(this Map)" : key);
          sb.append('=');
          sb.append(value == this ? "(this Map)" : value);
          if (!i.hasNext())
              return sb.append('}').toString();
          sb.append(',').append(' ');
      }
  }

  protected Object clone() throws CloneNotSupportedException {
      CompactAbstractMap<?, ?> result = (CompactAbstractMap<?, ?>) super.clone();
      return result;
  }

  public static class SimpleEntry<K, V>
          implements Entry<K, V>, java.io.Serializable {
      @java.io.Serial
      private static final long serialVersionUID = -8499721149061103585L;

      @SuppressWarnings("serial")
      private final K key;
      @SuppressWarnings("serial")
      private V value;

      public SimpleEntry(K key, V value) {
          this.key = key;
          this.value = value;
      }

      public SimpleEntry(Entry<? extends K, ? extends V> entry) {
          this.key = entry.getKey();
          this.value = entry.getValue();
      }

      public K getKey() {
          return key;
      }

      public V getValue() {
          return value;
      }

      public V setValue(V value) {
          V oldValue = this.value;
          this.value = value;
          return oldValue;
      }

      public boolean equals(Object o) {
          if (!(o instanceof Map.Entry))
              return false;
          Entry<?, ?> e = (Entry<?, ?>) o;
          return eq(key, e.getKey()) && eq(value, e.getValue());
      }

      public int hashCode() {
          return (key == null ? 0 : key.hashCode()) ^
                  (value == null ? 0 : value.hashCode());
      }

      public String toString() {
          return key + "=" + value;
      }

  }

  public static class SimpleImmutableEntry<K, V>
          implements Entry<K, V>, java.io.Serializable {
      @java.io.Serial
      private static final long serialVersionUID = 7138329143949025153L;

      @SuppressWarnings("serial")
      private final K key;
      @SuppressWarnings("serial")
      private final V value;

      public SimpleImmutableEntry(K key, V value) {
          this.key = key;
          this.value = value;
      }

      public SimpleImmutableEntry(Entry<? extends K, ? extends V> entry) {
          this.key = entry.getKey();
          this.value = entry.getValue();
      }

      public K getKey() {
          return key;
      }

      public V getValue() {
          return value;
      }

      public V setValue(V value) {
          throw new UnsupportedOperationException();
      }

      public boolean equals(Object o) {
          if (!(o instanceof Map.Entry))
              return false;
          Entry<?, ?> e = (Entry<?, ?>) o;
          return eq(key, e.getKey()) && eq(value, e.getValue());
      }

      public int hashCode() {
          return (key == null ? 0 : key.hashCode()) ^
                  (value == null ? 0 : value.hashCode());
      }

      public String toString() {
          return key + "=" + value;
      }
  }
}


abstract static class AbstractSteppable implements Steppable {
  public void run() { try { stepAll(this); } catch (Exception __e) { throw rethrow(__e); } }
}
static interface ILongQueue {
  public boolean isEmpty();
  public void add(long element);
  
  // return value is undefined if queue is empty
  public long poll();
}


// Note for implementors: It is allowed to call step() again
// after it returned false (usually it should just return false again)
static interface Steppable {
  public boolean step(); // return false if done
}


static boolean scaffoldingEnabled(Object o) {
  return metaGet(o, "scaffolding") != null;
}


static int area(Rect r) {
  return rectArea(r);
}

static double area(DoubleRect r) {
  return r == null ? 0 : r.w*r.h;
}


static int area(WidthAndHeight img) {
  return img == null ? 0 : img.getWidth()*img.getHeight();
}


static int area(BufferedImage img) {
  return img == null ? 0 : img.getWidth()*img.getHeight();
}



static void stepMaxWithStats(Steppable s, long maxSteps) {
  stepAllWithStats(s, maxSteps);
}

static void stepMaxWithStats(long maxSteps, Steppable s) {
  stepMaxWithStats(s, maxSteps);
}


static Rect rectFromPointsOrNull(int x1, int y1, int x2, int y2) {
  return nullIfEmptyRect(pointsRect(x1, y1, x2, y2));
}


static <A> Value<A> value(A a) {
  return new Value<A>(a);
}


static <A, B> boolean containsKey(Map<A, B> map, A key) {
  return map != null && map.containsKey(key);
}


static <A, B> Map.Entry<A, B> simpleMapEntry(A key, B value) {
  return new Map.Entry<A, B>() {
    public A getKey() { return key; }
    public B getValue() { return value; }
    public B setValue(B newValue) { throw unimplemented(); }
  };
}


static double fracNonNeg(double d) {
  return frac_nonNeg(d);
}


static double twoPi() {
  return Math.PI*2;
}


static String plusPrefixUnlessMinus(String s) {
  return startsWith(s, "-") ? s : "+" + s;
}


static Pt longToPt(long l) {
  return new Pt(firstIntFromLong(l), secondIntFromLong(l));
}


static long ptToLong(Pt p) {
  return p == null ? -1: intPairToLong(p.x, p.y);
}

static long ptToLong(int x, int y) {
  return intPairToLong(x, y);
}


static int modRange_incl(int i, int start, int end) {
  return start+mod(i-start, end-start+1);
}


static Pt onePathDirection(int index) {
  return onePathDirections()[index];
}

static Pt onePathDirection(Pt p, int index) {
  return ptPlus(p, onePathDirections()[index]);
}


static int lLongArray(long[] a) {
  return a == null ? 0 : a.length;
}


static long[] resizeLongArray(long[] a, int n) {
  if (n == lLongArray(a)) return a;
  long[] b = new long[n];
  arraycopy(a, 0, b, 0, Math.min(lLongArray(a), n));
  return b;
}


static <A> ArrayList<Long> longArrayToList(long[] a) {
  if (a == null) return null;
  return longArrayToList(a, 0, a.length);
}

// no range checking on from/to in the interest of S P E E E E E EEED
static <A> ArrayList<Long> longArrayToList(long[] a, int from, int to) {
  if (a == null) return null;
  ArrayList < Long > l = new ArrayList<>(to-from);
  for (int i = from; i < to; i++) l.add(a[i]);
  return l;
}


// returns number of steps
static long stepAll(Steppable s) {
  long steps = 0;
  if (s != null) {
    var pingSource = pingSource();
    while (true) {
      ping(pingSource);
      if (s.step())
        ++steps;
      else
        break;
    }
  }
  return steps;
}





static int rectArea(Rect r) {
  return r == null ? 0 : r.w*r.h;
}


static void stepAllWithStats(Steppable s) { stepAllWithStats(s, null); }
static void stepAllWithStats(Steppable s, Long maxSteps) {
  if (s == null) return;
  long n = 0;
  long time = sysNow();
  if (maxSteps == null)
    while  (s.step()) { ping(); ++n; }
  else
    while  (n < maxSteps && s.step()) { ping(); ++n; }
  time = sysNow()-time;
  print(n2(n, "step") + " in " + n2(time) + " ms");
}



static Rect nullIfEmptyRect(Rect r) {
  return rectEmpty(r) ? null : r;
}


static double frac_nonNeg(double d) {
  return mod(d, 1);
}


static int firstIntFromLong(long l) {
  return (int) (l >> 32);
}


static int secondIntFromLong(long l) {
  return (int) l;
}


static long intPairToLong(IntPair p) {
  return p == null ? 0 : (((long) p.a) << 32) | (((long) p.b) & 0xFFFFFFFF);
}

static long intPairToLong(int a, int b) {
  return (((long) a) << 32) | (((long) b) & 0xFFFFFFFF);
}


// better modulo that gives positive numbers always
static int mod(int n, int m) {
  return (n % m + m) % m;
}

static long mod(long n, long m) {
  return (n % m + m) % m;
}

static BigInteger mod(BigInteger n, int m) {
  return n.mod(bigint(m));
}

static double mod(double n, double m) {
  return (n % m + m) % m;
}



static Pt ptPlus(Pt a, Pt b) {
  return addPts(a, b);
}




static boolean rectEmpty(Rect r) {
  return r == null || r.w <= 0 || r.h <= 0;
}




static class Value<A> implements IF0<A> , IFieldsToList{
  A value;
  Value() {}
  Value(A value) {
  this.value = value;}

public boolean equals(Object o) {
if (!(o instanceof Value)) return false;
    Value __1 =  (Value) o;
    return eq(value, __1.value);
}

  public int hashCode() {
    int h = 82420049;
    h = boostHashCombine(h, _hashCode(value));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {value}; }

  public A get() { return value; }
  
  public String toString() { return str(get()); }
}
static final class IntPair implements Comparable<IntPair> , IFieldsToList{
  int a;
  int b;
  IntPair() {}
  IntPair(int a, int b) {
  this.b = b;
  this.a = a;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + a + ", " + b + ")"; }public Object[] _fieldsToList() { return new Object[] {a, b}; }

  public boolean equals(Object o) {
    if (!(o instanceof IntPair)) return false;
    IntPair x =  (IntPair) o;
    return a == x.a && b == x.b;
  }

  public int hashCode() {
    int h = -672893111;
    h = boostHashCombine(h, _hashCode(a));
    h = boostHashCombine(h, _hashCode(b));
    return h;
  }
  
  public int compareTo(IntPair p) {
    if (p == null) return 1;
    int pa = p.a;
    if (a < pa) return -1;
    if (a > pa) return 1;
    return Integer.compare(b, p.b);
  }
}
static class DoubleRect {
  double x, y, w, h;
  
  DoubleRect() {}
  DoubleRect(Rectangle r) {
    x = r.x;
    y = r.y;
    w = r.width;
    h = r.height;
  }
  DoubleRect(double x, double y, double w, double h) {
  this.h = h;
  this.w = w;
  this.y = y;
  this.x = x;}
  
  // Huh. not implementing equals()/hashCode? Stefan is mysterious
  boolean eq(Object o) {
    if (!(o instanceof DoubleRect)) return false;
    if (o == this) return true;
    DoubleRect r =  (DoubleRect) o;
    return x == r.x && y == r.y && w == r.w && h == r.h;
  }
  
  public String toString() {
    return x + "," + y + " / " + w + "," + h;
  }
  
  double x1() { return x; }
  double y1() { return y; }
  double x2() { return x + w; }
  double y2() { return y + h; }
  
  boolean contains(Pt p) {
    return contains(p.x, p.y);
  }
  
  boolean contains(double _x, double _y) {
    return _x >= x && _y >= y && _x < x+w && _y < y+h;
  }
  
  boolean empty() { return w <= 0 || h <= 0; }
}

}