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 LongRange intersectLongRanges(LongRange a, LongRange b) {
  long start = max(a.start, b.start);
  long end = min(a.end, b.end);
  return start <= end ? new LongRange(start, end) : null;
}
static int max(int a, int b) { return Math.max(a, b); }
static int max(int a, int b, int c) { return max(max(a, b), c); }
static long max(int a, long b) { return Math.max((long) a, b); }
static long max(long a, long b) { return Math.max(a, b); }
static double max(int a, double b) { return Math.max((double) a, b); }
static float max(float a, float b) { return Math.max(a, b); }
static double max(double a, double b) { return Math.max(a, b); }

static int max(Collection<Integer> c) {
  int x = Integer.MIN_VALUE;
  for (int i : c) x = max(x, i);
  return x;
}

static double max(double[] c) {
  if (c.length == 0) return Double.MIN_VALUE;
  double x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static float max(float[] c) {
  if (c.length == 0) return Float.MAX_VALUE;
  float x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static byte max(byte[] c) {
  byte x = -128;
  for (byte d : c) if (d > x) x = d;
  return x;
}

static short max(short[] c) {
  short x = -0x8000;
  for (short d : c) if (d > x) x = d;
  return x;
}

static int max(int[] c) {
  int x = Integer.MIN_VALUE;
  for (int d : c) if (d > x) x = d;
  return x;
}
static int min(int a, int b) {
  return Math.min(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }

static double min(double a, double b) {
  return Math.min(a, b);
}

static double min(double[] c) {
  double x = Double.MAX_VALUE;
  for (double d : c) x = Math.min(x, d);
  return x;
}

static float min(float[] c) {
  float x = Float.MAX_VALUE;
  for (float d : c) x = Math.min(x, d);
  return x;
}

static byte min(byte[] c) {
  byte x = 127;
  for (byte d : c) if (d < x) x = d;
  return x;
}

static short min(short[] c) {
  short x = 0x7FFF;
  for (short d : c) if (d < x) x = d;
  return x;
}

static int min(int[] c) {
  int x = Integer.MAX_VALUE;
  for (int d : c) if (d < x) x = d;
  return x;
}


final static class LongRange {
  long start, end;
  
  LongRange() {}
  LongRange(long start, long end) {
  this.end = end;
  this.start = start;}
  
  public boolean equals(Object o) {
    if (o instanceof LongRange) return start == ((LongRange) o).start && end == ((LongRange) o).end;
    return false;
  }
  
  public int hashCode() {
    return boostHashCombine(hashOfLong(start), hashOfLong(end));
  }
  
  long length() { return end-start; }
  
  static String _fieldOrder = "start end";
  
  public String toString() { return "[" + start + ";" + end + "]"; }
}

static int boostHashCombine(int a, int b) {
  return a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2));
}
static int hashOfLong(long l) {
  return Long.hashCode(l);
}
static int length(Object[] array) {
  return array == null ? 0 : array.length;
}

static int length(List list) {
  return list == null ? 0 : list.size();
}

static int length(String s) {
  return s == null ? 0 : s.length();
}

}