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 String formatDoubleRect(int digits, DoubleRect r) {
  return r == null ? str(r) : formatDouble(r.x, digits) + "/" + formatDouble(r.y, digits) + ", size: " + formatDouble(r.w, digits) + "/" + formatDouble(r.h, digits);
}
static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return new String(c);
}


static String formatDouble(double d, int digits) {
  String format = digits <= 0 ? "0" : "0." + rep(digits, '#');
  return decimalFormatEnglish(format, d);
}

static String formatDouble(double d) {
  return str(d);
}




static String rep(int n, char c) {
  return repeat(c, n);
}

static String rep(char c, int n) {
  return repeat(c, n);
}

static <A> List<A> rep(A a, int n) {
  return repeat(a, n);
}

static <A> List<A> rep(int n, A a) {
  return repeat(n, a);
}



static String decimalFormatEnglish(String format, double d) {
  return decimalFormatEnglish(format).format(d);
}

static java.text.DecimalFormat decimalFormatEnglish(String format) {
  return new java.text.DecimalFormat(format, new java.text.DecimalFormatSymbols(Locale.ENGLISH));
}




static String repeat(char c, int n) {
  n = Math.max(n, 0);
  char[] chars = new char[n];
  for (int i = 0; i < n; i++)
    chars[i] = c;
  return new String(chars);
}

static <A> List<A> repeat(A a, int n) {
  n = Math.max(n, 0);
  List<A> l = new ArrayList(n);
  for (int i = 0; i < n; i++)
    l.add(a);
  return l;
}

static <A> List<A> repeat(int n, A a) {
  return repeat(a, n);
}




static class DoubleRect {
  double x, y, w, h;
  
  DoubleRect() {}
  DoubleRect(Rectangle r) {
    x = r.x;
    y = r.y;
    w = r.width;
    h = r.height;
  }
  DoubleRect(double x, double y, double w, double h) {
  this.h = h;
  this.w = w;
  this.y = y;
  this.x = x;}
  
  // Huh. not implementing equals()/hashCode? Stefan is mysterious
  boolean eq(Object o) {
    if (!(o instanceof DoubleRect)) return false;
    if (o == this) return true;
    DoubleRect r =  (DoubleRect) o;
    return x == r.x && y == r.y && w == r.w && h == r.h;
  }
  
  public String toString() {
    return x + "," + y + " / " + w + "," + h;
  }
  
  double x1() { return x; }
  double y1() { return y; }
  double x2() { return x + w; }
  double y2() { return y + h; }
  
  boolean contains(Pt p) {
    return contains(p.x, p.y);
  }
  
  boolean contains(double _x, double _y) {
    return _x >= x && _y >= y && _x < x+w && _y < y+h;
  }
  
  boolean empty() { return w <= 0 || h <= 0; }
}


static class Pt implements Comparable<Pt> {
  int x, y;
  
  Pt() {}
  Pt(Point p) {
    x = p.x;
    y = p.y;
  }
  Pt(int x, int y) {
  this.y = y;
  this.x = x;}
  
  Point getPoint() {
    return new Point(x, y);
  }
  
  public boolean equals(Object o) {
    return o instanceof Pt && x == ((Pt) o).x && y == ((Pt) o).y;
  }
  
  public int hashCode() {
    return boostHashCombine(x, y);
  }
  
  // compare in scan order
  public int compareTo(Pt p) {
    if (y != p.y) return cmp(y, p.y);
    return cmp(x, p.x);
  }
  
  public String toString() {
    return x + ", " + y;
  }
}


static boolean contains(Collection c, Object o) {
  return c != null && c.contains(o);
}

static boolean contains(Object[] x, Object o) {
  if (x != null)
    for (Object a : x)
      if (eq(a, o))
        return true;
  return false;
}

static boolean contains(String s, char c) {
  return s != null && s.indexOf(c) >= 0;
}

static boolean contains(String s, String b) {
  return s != null && s.indexOf(b) >= 0;
}

static boolean contains(BitSet bs, int i) {
  return bs != null && bs.get(i);
}




static int boostHashCombine(int a, int b) {
  return a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2));
}


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 boolean eq(Object a, Object b) {
  return a == b || a != null && b != null && a.equals(b);
}





}