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> Pair<A, A> sortedPair(A a, A b) {
  return cmp(a, b) <= 0 ? pair(a, b) : pair(b, a);
}

static <A> Pair<A, A> sortedPair(Pair<A, A> p) {
  return p == null ? null : cmp(p.a, p.b) <= 0 ? p : reversePair(p);
}
static int cmp(Number a, Number b) {
  return a == null ? b == null ? 0 : -1 : cmp(a.doubleValue(), b.doubleValue());
}

static int cmp(double a, double b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(int a, int b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(long a, long b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(Object a, Object b) {
  if (a == null) return b == null ? 0 : -1;
  if (b == null) return 1;
  return ((Comparable) a).compareTo(b);
}

static <A, B> Pair<A, B> pair(A a, B b) {
  return new Pair(a, b);
}

static <A> Pair<A, A> pair(A a) {
  return new Pair(a, a);
}

static <A, B> Pair<B, A> reversePair(Pair<A, B> p) {
  return p == null ? null : pair(p.b, p.a);
}



static class Pair<A, B> implements Comparable<Pair<A, B>> {
  A a;
  B b;

  Pair() {}
  Pair(A a, B b) {
  this.b = b;
  this.a = a;}
  
  public int hashCode() {
    return hashCodeFor(a) + 2*hashCodeFor(b);
  }
  
  public boolean equals(Object o) {
    if (o == this) return true;
    if (!(o instanceof Pair)) return false;
    Pair t = (Pair) o;
    return eq(a, t.a) && eq(b, t.b);
  }
  
  public String toString() {
    return "<" + a + ", " + b + ">";
  }
  
  public int compareTo(Pair<A, B> p) {
    if (p == null) return 1;
    int i = ((Comparable<A>) a).compareTo(p.a);
    if (i != 0) return i;
    return ((Comparable<B>) b).compareTo(p.b);
  }
}

static int hashCodeFor(Object a) {
  return a == null ? 0 : a.hashCode();
}

static boolean eq(Object a, Object b) {
  return a == b || a != 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);
}


}