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 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 boolean isTrueOrYes(Object o) {
  return isTrueOpt(o) || o instanceof String && (eqicOneOf(((String) o), "1", "t", "true") || isYes(((String) o)));
}
static  LinkedHashMap asLinkedHashMap(Map map) {
  if (map instanceof LinkedHashMap) return (LinkedHashMap) map;
  LinkedHashMap m = new LinkedHashMap();
  if (map != null) synchronized(collectionMutex(map)) {
    m.putAll(map);
  }
  return m;
}
static boolean isTrueOpt(Object o) {
  if (o instanceof Boolean)
    return ((Boolean) o).booleanValue();
  return false;
}
static boolean eqicOneOf(String s, String... l) {
  for (String x : l) if (eqic(s, x)) return true; return false;
}
static List 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(get(parse3(s), 1))));
}
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 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(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  ArrayList 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 toLowerCase(List strings) {
  List 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();
}
// 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);
    }
      
    
      if (o instanceof DynamicObject)
        return ((DynamicObject) o).fieldValues.get(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 parse3(String s) {
  return dropPunctuation(javaTokPlusPeriod(s));
}
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;
}
static boolean eqOneOf(Object o, Object... l) {
  for (Object x : l) if (eq(o, x)) return true; return false;
}
static String asString(Object o) {
  return o == null ? null : o.toString();
}
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 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 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 asRuntimeException(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
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 List dropPunctuation_keep = ll("*", "<", ">");
static List dropPunctuation(List tok) {
  tok = new ArrayList(tok);
  for (int i = 1; i < tok.size(); i += 2) {
    String t = tok.get(i);
    if (t.length() == 1 && !Character.isLetter(t.charAt(0)) && !Character.isDigit(t.charAt(0)) && !dropPunctuation_keep.contains(t)) {
      tok.set(i-1, tok.get(i-1) + tok.get(i+1));
      tok.remove(i);
      tok.remove(i);
      i -= 2;
    }
  }
  return tok;
}
static String dropPunctuation(String s) {
  return join(dropPunctuation(nlTok(s)));
}
// This is made for NL parsing.
// It's javaTok extended with "..." token, "$n" and "#n" and
// special quotes (which are converted to normal ones).
static List javaTokPlusPeriod(String s) {
  List tok = new ArrayList();
  if (s == null) return tok;
  int l = s.length();
  
  int i = 0;
  while (i < l) {
    int j = i;
    char c; String cc;
    
    // scan for whitespace
    while (j < l) {
      c = s.charAt(j);
      cc = s.substring(j, Math.min(j+2, l));
      if (c == ' ' || c == '\t' || c == '\r' || c == '\n')
        ++j;
      else if (cc.equals("/*")) {
        do ++j; while (j < l && !s.substring(j, Math.min(j+2, l)).equals("*/"));
        j = Math.min(j+2, l);
      } else if (cc.equals("//")) {
        do ++j; while (j < l && "\r\n".indexOf(s.charAt(j)) < 0);
      } else
        break;
    }
    
    tok.add(s.substring(i, j));
    i = j;
    if (i >= l) break;
    c = s.charAt(i);
    cc = s.substring(i, Math.min(i+2, l));
    // scan for non-whitespace
    if (c == (char) 0x201C || c == (char) 0x201D) c = '"'; // normalize quotes
    if (c == '\'' || c == '"') {
      char opener = c;
      ++j;
      while (j < l) {
        char _c = s.charAt(j);
        if (_c == (char) 0x201C || _c == (char) 0x201D) _c = '"'; // normalize quotes
        if (_c == opener) {
          ++j;
          break;
        } else if (s.charAt(j) == '\\' && j+1 < l)
          j += 2;
        else
          ++j;
      }
      if (j-1 >= i+1) {
        tok.add(opener + s.substring(i+1, j-1) + opener);
        i = j;
        continue;
      }
    } else if (Character.isJavaIdentifierStart(c))
      do ++j; while (j < l && (Character.isJavaIdentifierPart(s.charAt(j)) || s.charAt(j) == '\'')); // for things like "this one's"
    else if (Character.isDigit(c))
      do ++j; while (j < l && Character.isDigit(s.charAt(j)));
    else if (cc.equals("[[")) {
      do ++j; while (j+1 < l && !s.substring(j, j+2).equals("]]"));
      j = Math.min(j+2, l);
    } else if (cc.equals("[=") && i+2 < l && s.charAt(i+2) == '[') {
      do ++j; while (j+2 < l && !s.substring(j, j+3).equals("]=]"));
      j = Math.min(j+3, l);
    } else if (s.substring(j, Math.min(j+3, l)).equals("..."))
      j += 3;
    else if (c == '$' || c == '#')
      do ++j; while (j < l && Character.isDigit(s.charAt(j)));
    else
      ++j;
    tok.add(s.substring(i, j));
    i = j;
  }
  
  if ((tok.size() % 2) == 0) tok.add("");
  return tok;
}
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);
  
    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 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  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 vmBus_send(String msg, Object... args) {
  Object arg = vmBus_wrapArgs(args);
  pcallFAll(vm_busListeners_live(), msg, arg);
  pcallFAll(vm_busListenersByMessage_live().get(msg), msg, arg);
}
static void vmBus_send(String msg) {
  vmBus_send(msg, (Object) null);
}
static void _handleError(Error e) {
  call(javax(), "_handleError", e);
}
static  List ll(A... a) {
  ArrayList l = new ArrayList(a.length);
  if (a != null) for (A x : a) l.add(x);
  return l;
}
public static  String join(String glue, Iterable strings) {
  if (strings == null) return "";
  if (strings instanceof Collection) {
    if (((Collection) strings).size() == 1) return str(first(((Collection) strings)));
  }
  StringBuilder buf = new StringBuilder();
  Iterator i = strings.iterator();
  if (i.hasNext()) {
    buf.append(i.next());
    while (i.hasNext())
      buf.append(glue).append(i.next());
  }
  return buf.toString();
}
public static String join(String glue, String... strings) {
  return join(glue, Arrays.asList(strings));
}
static  String join(Iterable strings) {
  return join("", strings);
}
static  String join(Iterable 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 List nlTok(String s) {
  return javaTokPlusPeriod(s);
}
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