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 static x30_pkg.x30_util.DynamicObject;
import java.awt.geom.*;
import java.text.*;
import java.text.NumberFormat;
import java.util.TimeZone;
class main {
static ![]() IImageRegion
 IImageRegion![]() g22_biggestRegionByBounds(Iterable> regions) {
  return highestBy(regions, r -> r.bounds().area());
}
static  A highestBy(Iterable l, Object f) {
  return highestByFunction(l, f);
}
static  A highestBy(Object f, Iterable l) {
  return highestByFunction(f, l);
}
static  A highestBy(Iterable l, IF1 f) {
  return highestByFunction(f, l);
}
static  A highestBy(IF1 f, Iterable l) {
  return highestByFunction(f, l);
}
static  A highestBy(IF1 f, A[] l) {
  return highestByFunction(f, wrapAsList(l));
}
static  A highestByFunction(Iterable l, Object f) {
  A best = null;
  Object bestValue = null;
  if (l != null) for (A a : l) {
    Object val = callF(f, a);
    if (best == null || cmp(val, bestValue) > 0) {
      best = a;
      bestValue = val;
    }
  }
  return best;
}
static  A highestByFunction(Object f, Iterable l) {
  return highestByFunction(l, f);
}
static  A highestByFunction(IF1 f, Iterable l) {
  return highestByFunction(l, (Object) f);
}
static  A highestByFunction(Iterable l, IF1 f) {
  return highestByFunction(f, l);
}
static  List wrapAsList(A[] a) {
  return wrapArrayAsList(a);
}
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 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  List wrapArrayAsList(A[] a) {
  return a == null ? null : Arrays.asList(a);
}
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 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(AppendableChain a) { return a == null ? 0 : a.size; }
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 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 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
 g22_biggestRegionByBounds(Iterable> regions) {
  return highestBy(regions, r -> r.bounds().area());
}
static  A highestBy(Iterable l, Object f) {
  return highestByFunction(l, f);
}
static  A highestBy(Object f, Iterable l) {
  return highestByFunction(f, l);
}
static  A highestBy(Iterable l, IF1 f) {
  return highestByFunction(f, l);
}
static  A highestBy(IF1 f, Iterable l) {
  return highestByFunction(f, l);
}
static  A highestBy(IF1 f, A[] l) {
  return highestByFunction(f, wrapAsList(l));
}
static  A highestByFunction(Iterable l, Object f) {
  A best = null;
  Object bestValue = null;
  if (l != null) for (A a : l) {
    Object val = callF(f, a);
    if (best == null || cmp(val, bestValue) > 0) {
      best = a;
      bestValue = val;
    }
  }
  return best;
}
static  A highestByFunction(Object f, Iterable l) {
  return highestByFunction(l, f);
}
static  A highestByFunction(IF1 f, Iterable l) {
  return highestByFunction(l, (Object) f);
}
static  A highestByFunction(Iterable l, IF1 f) {
  return highestByFunction(f, l);
}
static  List wrapAsList(A[] a) {
  return wrapArrayAsList(a);
}
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 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  List wrapArrayAsList(A[] a) {
  return a == null ? null : Arrays.asList(a);
}
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 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(AppendableChain a) { return a == null ? 0 : a.size; }
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 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 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