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[] intersectIntArrayAndBitSet(int[] array, BitSet bs) {
  if (array == null || bs == null) return null;
  int n = array.length;
  IntBuffer out = new IntBuffer(n);
  for (int i = 0; i < n; i++) {
    int x = array[i];
    if (bs.get(x))
      out.add(x);
  }
  return out.toArray();
}
static class IntBuffer {
  int[] data;
  int size;
  
  IntBuffer() {}
  IntBuffer(int size) { if (size != 0) data = new int[size]; }
  
  void add(int i) {
    if (size >= lIntArray(data))
      data = resizeIntArray(data, Math.max(1, lIntArray(data)*2));
    data[size++] = i;
  }
  
  int[] toArray() {
    return size == 0 ? null : resizeIntArray(data, size);
  }
  
  void reset() { size = 0; }
}

static int lIntArray(int[] a) {
  return a == null ? 0 : a.length;
}
static int[] resizeIntArray(int[] a, int n) {
  if (n == lIntArray(a)) return a;
  int[] b = new int[n];
  arraycopy(a, 0, b, 0, Math.min(lIntArray(a), n));
  return b;
}


static void arraycopy(Object[] a, Object[] b) {
  if (a != null && b != null)
    arraycopy(a, 0, b, 0, Math.min(a.length, b.length));
}

static void arraycopy(Object src, int srcPos, Object dest, int destPos, int n) {
  if (n != 0)
    System.arraycopy(src, srcPos, dest, destPos, n);
}

}