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 int[] bitSetToIntArray(BitSet bs) {
  if (bs == null) return null;
  int n = bs.cardinality();
  int[] result = new int[n];
  int j = 0;
  for (int i = bs.nextSetBit(0); i >= 0; i = bs.nextSetBit(i+1))
    result[j++] = i;
  return result;
}}