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;
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 AbstractWAndH extends Meta implements WidthAndHeight {
AbstractWAndH() {}
int w, h;
public int getWidth() { return w; }
public int getHeight() { return h; }
AbstractWAndH(int w, int h) {
this.h = h;
this.w = w;}
String sizeToString() { return n2(w) + "*" + n2(h) + " px"; }
}
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(double l, String singular) {
return empty(singular) ? str(l) : n2(l, singular, singular + "s");
}
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, singular + "s");
}
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, singular + "s"); }
static String n2(IMultiMap mm, String singular, String plural) {
return n_fancy2(l(mm), singular, plural);
}
static String formatWithThousands(long l) {
return formatWithThousandsSeparator(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 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(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 String str(Object o) {
return o == null ? "null" : o.toString();
}
static String str(char[] c) {
return 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 String formatWithThousandsSeparator(long l) {
return NumberFormat.getInstance(new Locale("en_US")).format(l);
}
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 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 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 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 RuntimeException asRuntimeException(Throwable t) {
if (t instanceof Error)
_handleError((Error) t);
return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static String getClassName(Object o) {
return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
static void _handleError(Error e) {
//call(javax(), '_handleError, e);
}
// 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(); }
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 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()); }
}
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 IFieldsToList {
Object[] _fieldsToList();
}
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 Pt implements Comparable, 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 interface IAutoCloseableF0 extends IF0, AutoCloseable {}
public static interface IF0 {
A get();
}
interface IDoublePt {
public double x_double();
public double y_double();
}
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 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 long longMul(long a, long b) {
return a*b;
}
static String joinNemptiesWithColon(String... strings) {
return joinNempties(": ", strings);
}
static String joinNemptiesWithColon(Collection 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 int _hashCode(Object a) {
return a == null ? 0 : a.hashCode();
}
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 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 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);
}
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 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 Map convertObjectMetaToMap(IMeta o) { return convertObjectMetaToMap(o, () -> makeObjectMetaMap()); }
static Map convertObjectMetaToMap(IMeta o, IF0