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 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 javax.imageio.*;
import java.math.*;
class main {
static  List syncListPlus(Collection l, A... more) {
  if (l == null) return asList(more);
  synchronized(collectionMutex(l)) {
    return concatLists(l, asList(more));
  }
}
// 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(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(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 Object collectionMutex(List l) {
  return l;
}
static Object collectionMutex(Object o) {
  
  if (o instanceof List) return o;
  
  String c = className(o);
  if (eq(c, "java.util.TreeMap$KeySet"))
    c = className(o = getOpt(o, "m"));
  else if (eq(c, "java.util.HashMap$KeySet"))
    c = className(o = get_raw(o, "this$0"));
  
  
  if (eqOneOf(c, "java.util.TreeMap$AscendingSubMap", "java.util.TreeMap$DescendingSubMap"))
    c = className(o = get_raw(o, "m"));
    
  
    
  
  return o;
}
static  List concatLists(Iterable... lists) {
  List l = new ArrayList();
  if (lists != null) for (Iterable list : lists)
    addAll(l, list);
  return l;
}
static  List concatLists(Collection extends Iterable> lists) {
  List l = new ArrayList();
  if (lists != null) for (Iterable list : lists)
    addAll(l, list);
  return l;
}
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 String className(Object o) {
  return getClassName(o);
}
static boolean eq(Object a, Object b) {
  return a == b || a != null && b != null && a.equals(b);
}
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;
}
// get purpose 1: access a list/array/map (safer version of x.get(y))
static  A get(List l, int idx) {
  return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}
// seems to conflict with other signatures
/*static  B get(Map map, A key) {
  ret map != null ? map.get(key) : null;
}*/
static  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);
    }
      
    
  } 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 eqOneOf(Object o, Object... l) {
  for (Object x : l) if (eq(o, x)) return true; return false;
}
static  void addAll(Collection c, Iterable b) {
  if (c != null && b != null) for (A a : b) c.add(a);
}
static  boolean addAll(Collection c, Collection b) {
  return c != null && b != null && c.addAll(b);
}
static  boolean addAll(Collection c, B... b) {
  return c != null && c.addAll(Arrays.asList(b));
}
static  Map addAll(Map a, Map extends A,? extends B> b) {
  if (a != null) a.putAll(b);
  return a;
}
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 int max(Collection c) {
  int x = Integer.MIN_VALUE;
  for (int i : c) x = max(x, i);
  return 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 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(Object o) {
  return o == null ? 0
    : o instanceof String ? l((String) o)
    : o instanceof Map ? l((Map) o)
    : o instanceof Collection ? l((Collection) o)
    : o instanceof Object[] ? l((Object[]) o)
    : o instanceof boolean[] ? l((boolean[]) o)
    : o instanceof byte[] ? l((byte[]) o)
    : o instanceof char[] ? l((char[]) o)
    : o instanceof short[] ? l((short[]) o)
    : o instanceof int[] ? l((int[]) o)
    : o instanceof float[] ? l((float[]) o)
    : o instanceof double[] ? l((double[]) o)
    : o instanceof long[] ? l((long[]) o)
    : (Integer) call(o, "size");
}
static String getClassName(Object o) {
  return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
static String str(Object o) {
  return o == null ? "null" : o.toString();
}
static String str(char[] c) {
  return new String(c);
}
//static final Map> 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> getOpt_cache = _registerDangerousWeakMap(synchroMap(new getOpt_Map()));
//static final Map> getOpt_cache = _registerWeakMap(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 Object getOpt_cached(Object o, String field) { try {
  if (o == null) return null;
  Class c = o.getClass();
  HashMap map;
  synchronized(getOpt_cache) {
    map = getOpt_cache.get(c);
    if (map == null)
      map = getOpt_makeCache(c);
  }
  
  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);
  
  return null;
} catch (Exception __e) { throw rethrow(__e); } }
// used internally - we are in synchronized block
static HashMap getOpt_makeCache(Class c) {
  HashMap 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 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 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  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 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 void clear(Collection c) {
  if (c != null) c.clear();
}
static void clear(Map map) {
  if (map != null) map.clear();
}
static  void put(Map map, A a, B b) {
  if (map != null) map.put(a, b);
}
static  void put(List l, int i, A a) {
  if (l != null && i >= 0 && i < l(l)) l.set(i, a);
}
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