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.*;


//!include #1010605 // WeakHashMap2

class main {
static class Symbol {
  String text;
  boolean test;

  Symbol() {}
  Symbol(String text, boolean test) {
  this.test = test;
  this.text = text;} // weird signature to prevent accidental calling
  
  public int hashCode() { return main.hashCode(text); }
  public String toString() { return text; }
  public boolean equals(Object o) {
    if (!test) return this == o;
    return o instanceof Symbol && eq(text, ((Symbol) o).text);
  }
}

static WeakHashMap<Symbol,Boolean> symbolMap = new WeakHashMap();

static Symbol symbol(String s) {
  if (s == null) return null;
  synchronized(symbolMap) {
    Symbol test = new Symbol(s, true);
    //WeakHashMap2.Entry<Symbol, Bool> e = symbolMap.getEntry(test);
    //Symbol sym = e == null ? null : e.get();
    Object e = call(symbolMap, "getEntry", test);
    Symbol sym = (Symbol) ( callOpt(e, "get"));
    if (sym == null)
      symbolMap.put(sym = new Symbol(s, false), Boolean.TRUE);
    return sym;
  }
}

public static void main(final String[] args) throws Exception {
  Symbol a = symbol("a");
  Symbol a2 = symbol("a");
  assertEquals("a", str(a));
  assertEquals("a", str(a2));
  assertIdentical(a, a2);
  Symbol b = symbol("b");
  assertEquals("b", str(b));
}
  static Object call(Object o) {
    return callFunction(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) {
    try {
      if (o instanceof Class) {
        Method m = call_findStaticMethod((Class) o, method, args, false);
        m.setAccessible(true);
        return m.invoke(null, args);
      } else {
        Method m = call_findMethod(o, method, args, false);
        m.setAccessible(true);
        return m.invoke(o, args);
      }
    } catch (Exception e) {
      throw e instanceof RuntimeException ? (RuntimeException) e : new RuntimeException(e);
    }
  }

  static Method call_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
    Class _c = c;
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (!m.getName().equals(method)) {
          if (debug) System.out.println("Method name mismatch: " + method);
          continue;
        }

        if ((m.getModifiers() & Modifier.STATIC) == 0 || !call_checkArgs(m, args, debug))
          continue;

        return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (static) with " + args.length + " parameter(s) not found in " + _c.getName());
  }

  static Method call_findMethod(Object o, String method, Object[] args, boolean debug) {
    Class c = o.getClass();
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (m.getName().equals(method) && call_checkArgs(m, args, debug))
          return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (non-static) with " + args.length + " parameter(s) not found in " + o.getClass().getName());
  }

  private static boolean call_checkArgs(Method m, Object[] args, boolean debug) {
    Class<?>[] types = m.getParameterTypes();
    if (types.length != args.length) {
      if (debug)
        System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
      return false;
    }
    for (int i = 0; i < types.length; i++)
      if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
        if (debug)
          System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
        return false;
      }
    return true;
  }


static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return new String(c);
}
static void assertIdentical(String msg, Object a, Object b) {
  if (a != b)
    throw fail(msg);
}

static void assertIdentical(Object a, Object b) {
  if (a != b)
    throw fail();
}
static RuntimeException asRuntimeException(Throwable t) {
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static int hashCode(Object a) {
  return a == null ? 0 : a.hashCode();
}
static Object callOpt(Object o) {
  if (o == null) return null;
  return callF(o);
}

static Object callOpt(Object o, String method, Object... args) {
  try {
    if (o == null) return null;
    if (o instanceof Class) {
      Method m = callOpt_findStaticMethod((Class) o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(null, args);
    } else {
      Method m = callOpt_findMethod(o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(o, args);
    }
  } catch (Exception e) {
    //fail(e.getMessage() + " | Method: " + method + ", receiver: " + className(o) + ", args: (" + join(", ", map(f className, args) + ")");
    throw new RuntimeException(e);
  }
}

static Method callOpt_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
  Class _c = c;
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (!m.getName().equals(method)) {
        if (debug) System.out.println("Method name mismatch: " + method);
        continue;
      }

      if ((m.getModifiers() & Modifier.STATIC) == 0 || !callOpt_checkArgs(m, args, debug))
        continue;

      return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

static Method callOpt_findMethod(Object o, String method, Object[] args, boolean debug) {
  Class c = o.getClass();
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (m.getName().equals(method) && callOpt_checkArgs(m, args, debug))
        return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

private static boolean callOpt_checkArgs(Method m, Object[] args, boolean debug) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != args.length) {
    if (debug)
      System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
    return false;
  }
  for (int i = 0; i < types.length; i++)
    if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
      if (debug)
        System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
      return false;
    }
  return true;
}


static boolean equals(Object a, Object b) {
  return a == null ? b == null : a.equals(b);
}
static Map<Thread, Boolean> _registerThread_threads = Collections.synchronizedMap(new WeakHashMap());

static Thread _registerThread(Thread t) {
  _registerThread_threads.put(t, true);
  return t;
}

static void _registerThread() { _registerThread(Thread.currentThread()); }
static <A> A assertEquals(Object x, A y) {
  return assertEquals(null, x, y);
}

static <A> A assertEquals(String msg, Object x, A y) {
  if (!(x == null ? y == null : x.equals(y)))
    throw fail((msg != null ? msg + ": " : "") + y + " != " + x);
  return y;
}
static boolean eq(Object a, Object b) {
  return a == null ? b == null : a == b || a.equals(b);
}


// extended over Class.isInstance() to handle primitive types
static boolean isInstanceX(Class type, Object arg) {
  if (type == boolean.class) return arg instanceof Boolean;
  if (type == int.class) return arg instanceof Integer;
  if (type == long.class) return arg instanceof Long;
  if (type == float.class) return arg instanceof Float;
  if (type == short.class) return arg instanceof Short;
  if (type == char.class) return arg instanceof Character;
  if (type == byte.class) return arg instanceof Byte;
  if (type == double.class) return arg instanceof Double;
  return type.isInstance(arg);
}
static WeakHashMap<Class, ArrayList<Method>> callF_cache = new WeakHashMap();

static <A> A callF(F0<A> f) {
  return f == null ? null : f.get();
}

static Object callF(Object f, Object... args) { try {
  if (f instanceof String)
    return callMC((String) f, args);
  if (f instanceof Runnable) {
    ((Runnable) f).run();
    return null;
  }
  if (f == null) return null;
  
  Class c = f.getClass();
  ArrayList<Method> methods;
  synchronized(callF_cache) {
    methods = callF_cache.get(c);
    if (methods == null)
      methods = callF_makeCache(c);
  }
  
  int n = l(methods);
  if (n == 0) throw fail("No get method in " + getClassName(c));
  if (n == 1) return methods.get(0).invoke(f, args);
  for (int i = 0; i < n; i++) {
    Method m = methods.get(i);
    if (call_checkArgs(m, args, false))
      return m.invoke(f, args);
  }
  throw fail("No matching get method in " + getClassName(c));
} catch (Exception __e) { throw rethrow(__e); } }

// used internally
static ArrayList<Method> callF_makeCache(Class c) {
  ArrayList<Method> l = new ArrayList();
  Class _c = c;
  do {
    for (Method m : _c.getDeclaredMethods())
      if (m.getName().equals("get")) {
        m.setAccessible(true);
        l.add(m);
      }
    if (!l.isEmpty()) break;
    _c = _c.getSuperclass();
  } while (_c != null);
  callF_cache.put(c, l);
  return l;
}
static Object callFunction(Object f, Object... args) {
  return callF(f, args);
}
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(String msg) { throw new RuntimeException(msg == null ? "" : msg); }
static RuntimeException fail(String msg, Throwable innerException) { throw new RuntimeException(msg, innerException); }



static RuntimeException rethrow(Throwable e) {
  throw asRuntimeException(e);
}
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(int[] a) { return a == null ? 0 : a.length; }
static int l(float[] 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(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 instanceof String ? l((String) o)
    : o instanceof Map ? l((Map) o)
    : l((Collection) o); // incomplete
}




static final HashMap<String, List<Method>> callMC_cache = new HashMap();
static String callMC_key;
static Method callMC_value;

// varargs assignment fixer for a single string array argument
static Object callMC(String method, String[] arg) {
  return callMC(method, new Object[] {arg});
}

static Object callMC(String method, Object... args) { try {
  Method me;
  synchronized(callMC_cache) {
    me = method == callMC_key ? callMC_value : null;
  }
  if (me != null) return callMC_value.invoke(null, args);

  List<Method> m;
  synchronized(callMC_cache) {
    m = callMC_cache.get(method);
  }
  if (m == null) {
    if (callMC_cache.isEmpty()) {
      callMC_makeCache();
      m = callMC_cache.get(method);
    }
    if (m == null) throw fail("Method named " + method + " not found in main");
  }
  int n = m.size();
  if (n == 1) {
    me = m.get(0);
    synchronized(callMC_cache) {
      callMC_key = method;
      callMC_value = me;
    }
    return me.invoke(null, args);
  }
  for (int i = 0; i < n; i++) {
    me = m.get(i);
    if (call_checkArgs(me, args, false))
      return me.invoke(null, args);
  }
  throw fail("No method called " + method + " with matching arguments found in main");
} catch (Exception __e) { throw rethrow(__e); } }

static void callMC_makeCache() {
  synchronized(callMC_cache) {
    callMC_cache.clear();
    Class _c = (Class) mc(), c = _c;
    while (c != null) {
      for (Method m : c.getDeclaredMethods())
        if ((m.getModifiers() & Modifier.STATIC) != 0) {
          m.setAccessible(true);
          multiMapPut(callMC_cache, m.getName(), m);
        }
      c = c.getSuperclass();
    }
  }
}
static String getClassName(Object o) {
  return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}


static Class mc() {
  return main.class;
}
static <A, B> void multiMapPut(Map<A, List<B>> map, A a, B b) {
  List<B> l = map.get(a);
  if (l == null)
    map.put(a, l = new ArrayList());
  l.add(b);
}


static abstract class F0<A> {
  abstract A get();
}

// get purpose 1: access a list/array/map (safer version of x.get(y))

static <A> A get(List<A> l, int idx) {
  return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}

// seems to conflict with other signatures
/*static <A, B> B get(Map<A, B> map, A key) {
  ret map != null ? map.get(key) : null;
}*/

static <A> 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 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) {
      f.setAccessible(true);
      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(Object o, String field) {
  try {
    Field f = get_findField(o.getClass(), field);
    f.setAccessible(true);
    return f.get(o);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Object get(Class c, String field) {
  try {
    Field f = get_findStaticField(c, field);
    f.setAccessible(true);
    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() & 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 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;
}

}