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;
// has equals semantics so passing it to onChange() etc is idempotent
import static x30_pkg.x30_util.DynamicObject;
import java.text.*;
import java.text.NumberFormat;
import java.util.TimeZone;
import java.awt.geom.*;
class main {
static class UpdateTrigger implements Runnable , IFieldsToList{
  Updateable target;
  UpdateTrigger() {}
  UpdateTrigger(Updateable target) {
  this.target = target;}
  public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + target + ")"; }
public boolean equals(Object o) {
if (!(o instanceof UpdateTrigger)) return false;
    UpdateTrigger __1 =  (UpdateTrigger) o;
    return eq(target, __1.target);
}
  public int hashCode() {
    int h = -1756880753;
    h = boostHashCombine(h, _hashCode(target));
    return h;
  }
  public Object[] _fieldsToList() { return new Object[] {target}; }
  public void run() { try { { if (target != null) target.update(); } } catch (Exception __e) { throw rethrow(__e); } }
}
static String shortClassName_dropNumberPrefix(Object o) {
  return dropNumberPrefix(shortClassName(o));
}
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 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 int _hashCode(Object a) {
  return a == null ? 0 : a.hashCode();
}
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 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 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 void _handleError(Error e) {
  //call(javax(), '_handleError, 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  List dropFirst(List l) {
  return dropFirst(1, l);
}
static  List dropFirst(int n, Iterable i) { return dropFirst(n, toList(i)); }
static  List dropFirst(Iterable i) { return dropFirst(toList(i)); }
static  List dropFirst(int n, List l) {
  return n <= 0 ? l : new ArrayList(l.subList(Math.min(n, l.size()), l.size()));
}
static  List dropFirst(List 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  Chain dropFirst(Chain 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 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  List drop(Iterable 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  List drop(Iterable c, F1 pred) {
  return antiFilter(c, pred);
}
static  List drop(F1 pred, Iterable c) {
  return antiFilter(pred, c);
}
static  List drop(Iterable c, IF1 pred) {
  return antiFilter(c, pred);
}
static  List drop(IF1 pred, Iterable c) {
  return antiFilter(pred, c);
}
static  ArrayList toList(A[] a) { return asList(a); }
static ArrayList toList(int[] a) { return asList(a); }
static ArrayList toList(short[] a) { return asList(a); }
static ArrayList toList(long[] a) { return asList(a); }
static  ArrayList toList(Set s) { return asList(s); }
static  ArrayList toList(Iterable 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 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(IntSize o) { return o == null ? 0 : o.size(); }
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  int lastIndexOf(List 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  int lastIndexOf(List 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  List antiFilter(Iterable c, Object pred) {
  if (pred instanceof F1) return antiFilter(c, (F1) 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  List antiFilter(Iterable c, F1 pred) {
  List x = new ArrayList();
  if (c != null) for (B o : c)
    if (!pred.get(o).booleanValue())
      x.add(o);
  return x;
}
static  List antiFilter(F1 pred, Iterable c) {
  return antiFilter(c, pred);
}
static  List antiFilter(Iterable c, IF1 pred) {
  List x = new ArrayList();
  if (c != null) for (B o : c)
    if (!pred.get(o).booleanValue())
      x.add(o);
  return x;
}
static  List antiFilter(IF1 pred, Iterable c) {
  return antiFilter(c, pred);
}
// unclear semantics as to whether return null on null
static  ArrayList asList(A[] a) {
  return a == null ? new ArrayList() : new ArrayList(Arrays.asList(a));
}
static ArrayList asList(char[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (var i : a) l.add(i);
  return l;
}
static ArrayList asList(byte[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (var i : a) l.add(i);
  return l;
}
static ArrayList asList(int[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (int i : a) l.add(i);
  return l;
}
static ArrayList asList(long[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (long i : a) l.add(i);
  return l;
}
static ArrayList asList(float[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (float i : a) l.add(i);
  return l;
}
static ArrayList asList(double[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (double i : a) l.add(i);
  return l;
}
static ArrayList asList(short[] a) {
  if (a == null) return null;
  ArrayList l = emptyList(a.length);
  for (short i : a) l.add(i);
  return l;
}
static  ArrayList asList(Iterator it) {
  ArrayList l = new ArrayList();
  if (it != null)
    while (it.hasNext())
      l.add(it.next());
  return l;  
}
// disambiguation
static  ArrayList asList(IterableIterator s) {
  return asList((Iterator) s);
}
static  ArrayList asList(Iterable 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  ArrayList asList(Enumeration e) {
  ArrayList l = new ArrayList();
  if (e != null)
    while (e.hasMoreElements())
      l.add(e.nextElement());
  return l;
}
static  ArrayList asList(ReverseChain c) {
  return c == null ? emptyList() : c.toList();
}
static  List asList(Pair p) {
  return p == null ? null : ll(p.a, p.b);
}
static int strL(String s) {
  return s == null ? 0 : s.length();
}
static int lCharSequence(CharSequence s) {
  return s == null ? 0 : s.length();
}
static  int iteratorCount_int_close(Iterator 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 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 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 Map> callF_cache = newDangerousWeakHashMap();
  static  A callF(F0 f) {
    return f == null ? null : f.get();
  }
  static  B callF(F1 f, A a) {
    return f == null ? null : f.get(a);
  }
  static  A callF(IF0 f) {
    return f == null ? null : f.get();
  }
  static  B callF(IF1 f, A a) {
    return f == null ? null : f.get(a);
  }
static  B callF(A a, IF1 f) {
  return f == null ? null : f.get(a);
}
  static  void callF(VF1 f, A a) {
    if (f != null) f.get(a);
  }
static  void callF(A a, IVF1 f) {
  if (f != null) f.get(a);
}
static  void callF(IVF1 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 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 callF_makeCache(Class c) {
  ArrayList 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  List wrapArrayAsList(A[] a) {
  return a == null ? null : Arrays.asList(a);
}
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  ArrayList emptyList(Class c) {
  return new ArrayList();
}
static  List ll(A... a) {
  ArrayList l = new ArrayList(a.length);
  if (a != null) for (A x : a) l.add(x);
  return l;
}
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 getClassName(Object o) {
  return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
static  Map newDangerousWeakHashMap() {
  return _registerDangerousWeakMap(synchroMap(new WeakHashMap()));
}
// initFunction: voidfunc(Map) - is called initially, and after clearing the map
static  Map 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 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 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 max (Iterable 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 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 max(A a, A b) {
  return cmp(a, b) >= 0 ? a : b;
}
static RuntimeException asRuntimeException(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static List _registerDangerousWeakMap_preList;
static  A _registerDangerousWeakMap(A map) {
  return _registerDangerousWeakMap(map, null);
}
static  A _registerDangerousWeakMap(A map, Object init) {
  
  callF(init, map);
  
  if (init instanceof String) {
    final String f =  (String) init;
    init = new VF1