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.*;
// Calculates the fuzzy match of needle in haystack,
// using a modified version of the Levenshtein distance algorithm.
// ported from: http://ginstrom.com/scribbles/2007/12/01/fuzzy-substring-matching-with-levenshtein-distance-in-python/

class main {

static Pair<Integer, Integer> levenSubstringIC_withIndex(String haystack, String needle) {
  int m = strL(needle), n = strL(haystack);

  // base cases
  if (m == 1) {
    int idx = indexOfIC(haystack, needle);
    return idx < 0 ? pair(0, 1) : pair(idx, 0);
  }
  if (m == 0)
    return pair(0, m);

  int[] row1 = new int[n+1], row2 = new int[n+1];
  for (int i = 0; i < m; i++) {
    row2[0] = i+1;
    for (int j = 0; j < n; j++) {
      int cost = neqic(needle.charAt(i), haystack.charAt(j)) ? 1 : 0;
      row2[j+1] = min3(row1[j+1]+1,   // deletion
                       row2[j]+1,     // insertion
                       row1[j]+cost); // substitution
    }
    int[] temp = row1;
    row1 = row2;
    row2 = temp;
  }
  Pair<Integer, Integer> p = minOfIntArray_withIndex(row1);
  return pair(max(0, p.a-m), p.b);
}
static int strL(String s) {
  return s == null ? 0 : s.length();
}
static int indexOfIC(List<String> a, String b) {
  return indexOfIgnoreCase(a, b);
}

static int indexOfIC(List<String> a, String b, int i) {
  return indexOfIgnoreCase(a, b, i);
}

static int indexOfIC(String a, String b) {
  return indexOfIgnoreCase(a, 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 boolean neqic(String a, String b) {
  return !eqic(a, b);
}

static boolean neqic(char a, char b) {
  return !eqic(a, b);
}
static int min3(int a, int b, int c) {
  return min(min(a, b), c);
}
// return index and value
static Pair<Integer, Integer> minOfIntArray_withIndex(int[] a) {
  if (a == null || a.length == 0) return null;
  int n = a.length, x = a[0], best = 0;
  for (int i = 1; i < n; i++) {
    int y = a[i];
    if (y < x) {
      x = y;
      best = i;
    }
  }
  return pair(best, x);
}
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;
}


// works on lists and strings and null

static int indexOfIgnoreCase(List<String> a, String b) {
  return indexOfIgnoreCase(a, b, 0);
}

static int indexOfIgnoreCase(List<String> a, String b, int i) {
  int n = a == null ? 0 : a.size();
  for (; i < n; i++)
    if (eqic(a.get(i), b)) return i;
  return -1;
}

static int indexOfIgnoreCase(String a, String b) {
  return indexOfIgnoreCase_manual(a, b);
  /*Matcher m = Pattern.compile(b, Pattern.CASE_INSENSITIVE + Pattern.LITERAL).matcher(a);
  if (m.find()) return m.start(); else ret -1;*/
}
static boolean eqic(String a, String b) {
  
  
    if ((a == null) != (b == null)) return false;
    if (a == null) return true;
    return a.equalsIgnoreCase(b);
  
}



static boolean eqic(char a, char b) {
  if (a == b) return true;
  
    char u1 = Character.toUpperCase(a);
    char u2 = Character.toUpperCase(b);
    if (u1 == u2) return true;
  
  return Character.toLowerCase(u1) == Character.toLowerCase(u2);
}
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;
}


static int indexOfIgnoreCase_manual(String a, String b) {
  int la = strL(a), lb = strL(b);
  if (la < lb) return -1;
  int n = la-lb;
  
  loop: for (int i = 0; i <= n; i++) {
    for (int j = 0; j < lb; j++) {
      char c1 = a.charAt(i+j), c2 = b.charAt(j);
      if (!eqic(c1, c2))
        continue loop;
    }
    return i;
  }
  return -1;
}
static boolean eq(Object a, Object b) {
  return a == null ? b == null : a == b || b != null && a.equals(b);
}


static String asString(Object o) {
  return o == null ? null : o.toString();
}


static String str(Object o) {
  return o == null ? "null" : o.toString();
}

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


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();
}

}