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 <A, B> boolean mapPutOrRemove_trueIfChanged(Map<A, B> map, A key, B value) {
  if (value != null)
    return mapPut_trueIfChanged(map, key, value);
  if (map == null || key == null) return false;
  return map.remove(key) != null;
}
static <A, B> boolean mapPut_trueIfChanged(Map<A, B> map, A key, B value) {
  if (map != null && key != null && value != null)
    if (eq(map.get(key), value)) return false;
    else { map.put(key, value); return true; }
  return false;
}


static boolean eq(Object a, Object b) {
  return a == b || (a == null ? b == null : b != null && a.equals(b));
}




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

static String str(char[] c) {
  return new String(c);
}

}