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 boolean setBit_trueIfChanged(BitSet b, int bit) { return setBit_trueIfChanged(b, bit, true); }
static boolean setBit_trueIfChanged(BitSet b, int bit, boolean value) {
  if (b == null || b.get(bit) == value) return false;
  b.set(bit, value);
  return true;
}}