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.*;
public class main {


static List<String> strings = splitAtSpace("a b ab ba aab aba bbaa abc ca bac aabb eec ec cae eeaaee ebbbee aa bbccaa aaccccc");

public static void main(final String[] args) throws Exception {
  for (String a : strings)
    for (String b : strings) {
      int lev = leven(a, b);
      for (int max = 0; max <= lev+1; max++) {
        int i = leven_limited(a, b, max);
        if (i != min(lev, max))
          print("ERROR: " + quote(a) + " " + quote(b) + " " + lev + " " + " max " + max + " => " + i);
      }
    }
  print("done (" + l(strings)*l(strings) + " tests)");
}


static volatile StringBuffer local_log = new StringBuffer(); // not redirected
static volatile StringBuffer print_log = local_log; // might be redirected, e.g. to main bot

// in bytes - will cut to half that
static volatile int print_log_max = 1024*1024;
static volatile int local_log_max = 100*1024;
//static int print_maxLineLength = 0; // 0 = unset

static boolean print_silent; // total mute if set

static volatile ThreadLocal print_byThread; // special handling by thread

static void print() {
  print("");
}

// slightly overblown signature to return original object...
static <A> A print(A o) {
  ping();
  if (print_silent) return o;
  String s = String.valueOf(o) + "\n";
  print_noNewLine(s);
  return o;
}

static void print_noNewLine(String s) {
  if (print_byThread != null) {
    Object f = print_byThread.get();
    if (f != null)
      if (isFalse(callF(f, s))) return;
  }
  
  print_raw(s);
}

static void print_raw(String s) {
  s = fixNewLines(s);
  // TODO if (print_maxLineLength != 0)
  StringBuffer loc = local_log;
  StringBuffer buf = print_log;
  int loc_max = print_log_max;
  if (buf != loc && buf != null) {
    print_append(buf, s, print_log_max);
    loc_max = local_log_max;
  }
  if (loc != null) 
    print_append(loc, s, loc_max);
  System.out.print(s);
}

static void print(long l) {
  print(String.valueOf(l));
}

static void print(char c) {
  print(String.valueOf(c));
}

static void print_append(StringBuffer buf, String s, int max) {
  synchronized(buf) {
    buf.append(s);
    max /= 2;
    if (buf.length() > max) try {
      int newLength = max/2;
      int ofs = buf.length()-newLength;
      String newString = buf.substring(ofs);
      buf.setLength(0);
      buf.append("[...] ").append(newString);
    } catch (Exception e) {
      buf.setLength(0);
    }
  }
}
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 String quote(Object o) {
  if (o == null) return "null";
  return quote(str(o));
}

static String quote(String s) {
  if (s == null) return "null";
  StringBuilder out = new StringBuilder();
  quote_impl(s, out);
  return out.toString();
}
  
static void quote_impl(String s, StringBuilder out) {
  out.append('"');
  int l = s.length();
  for (int i = 0; i < l; i++) {
    char c = s.charAt(i);
    if (c == '\\' || c == '"')
      out.append('\\').append(c);
    else if (c == '\r')
      out.append("\\r");
    else if (c == '\n')
      out.append("\\n");
    else
      out.append(c);
  }
  out.append('"');
}
static int leven_limited(String left, String right, int threshold) {
  if (--threshold < 0) return 0;
  left = unnull(left);
  right = unnull(right);

  int n = left.length(); // length of left
  int m = right.length(); // length of right

  // if one string is empty, the edit distance is necessarily the length
  // of the other
  if (n == 0) {
      return m <= threshold ? m : threshold+1;
  } else if (m == 0) {
      return n <= threshold ? n : threshold+1;
  }

  if (n > m) {
      // swap the two strings to consume less memory
      final String tmp = left;
      left = right;
      right = tmp;
      n = m;
      m = right.length();
  }

  int[] p = new int[n + 1]; // 'previous' cost array, horizontally
  int[] d = new int[n + 1]; // cost array, horizontally
  int[] tempD; // placeholder to assist in swapping p and d

  // fill in starting table values
  final int boundary = Math.min(n, threshold) + 1;
  for (int i = 0; i < boundary; i++) {
      p[i] = i;
  }
  // these fills ensure that the value above the rightmost entry of our
  // stripe will be ignored in following loop iterations
  Arrays.fill(p, boundary, p.length, Integer.MAX_VALUE);
  Arrays.fill(d, Integer.MAX_VALUE);

  // iterates through t
  for (int j = 1; j <= m; j++) {
      final char rightJ = right.charAt(j - 1); // jth character of right
      d[0] = j;

      // compute stripe indices, constrain to array size
      final int min = Math.max(1, j - threshold);
      final int max = j > Integer.MAX_VALUE - threshold ? n : Math.min(
              n, j + threshold);

      // the stripe may lead off of the table if s and t are of different
      // sizes
      if (min > max) {
          return threshold+1;
      }

      // ignore entry left of leftmost
      if (min > 1) {
          d[min - 1] = Integer.MAX_VALUE;
      }

      // iterates through [min, max] in s
      for (int i = min; i <= max; i++) {
          if (left.charAt(i - 1) == rightJ) {
              // diagonally left and up
              d[i] = p[i - 1];
          } else {
              // 1 + minimum of cell to the left, to the top, diagonally
              // left and up
              d[i] = 1 + Math.min(Math.min(d[i - 1], p[i]), p[i - 1]);
          }
      }

      // copy current distance counts to 'previous row' distance counts
      tempD = p;
      p = d;
      d = tempD;
  }

  // if p[n] is greater than the threshold, there's no guarantee on it
  // being the correct
  // distance
  if (p[n] <= threshold) {
      return p[n];
  }
  return threshold+1;
}
static List<String> splitAtSpace(String s) {
  return asList(s.split("\\s+"));
}
static int leven(String s, String t) {
  // degenerate cases
  if (s.equals(t)) return 0;
  if (s.length() == 0) return t.length();
  if (t.length() == 0) return s.length();

  // create two work vectors of integer distances
  int[] v0 = new int[t.length() + 1];
  int[] v1 = new int[t.length() + 1];

  // initialize v0 (the previous row of distances)
  // this row is A[0][i]: edit distance for an empty s
  // the distance is just the number of characters to delete from t
  for (int i = 0; i < v0.length; i++)
      v0[i] = i;

  for (int i = 0; i < s.length(); i++)
  {
      // calculate v1 (current row distances) from the previous row v0

      // first element of v1 is A[i+1][0]
      //   edit distance is delete (i+1) chars from s to match empty t
      v1[0] = i + 1;

      // use formula to fill in the rest of the row
      for (int j = 0; j < t.length(); j++)
      {
          int cost = s.charAt(i) == t.charAt(j) ? 0 : 1;
          v1[j + 1] = Math.min(Math.min(v1[j] + 1, v0[j + 1] + 1), v0[j] + cost);
      }

      // copy v1 (current row) to v0 (previous row) for next iteration
      /*for (int j = 0; j < v0.length; j++)
          v0[j] = v1[j];*/
          
      // swap arrays
      int[] v = v1; v1 = v0; v0 = v;
  }

  // for array copying:
  // return v1[t.length()];
  // for array swapping:
  return v0[t.length()];
}
static int l(Object[] a) { return a == null ? 0 : a.length; }
static int l(boolean[] a) { return a == null ? 0 : a.length; }
static int l(byte[] a) { return a == null ? 0 : a.length; }
static int l(int[] a) { return a == null ? 0 : a.length; }
static int l(float[] a) { return a == null ? 0 : a.length; }
static int l(char[] a) { return a == null ? 0 : a.length; }
static int l(Collection c) { return c == null ? 0 : c.size(); }
static int l(Map m) { return m == null ? 0 : m.size(); }
static int l(CharSequence s) { return s == null ? 0 : s.length(); } static long l(File f) { return f == null ? 0 : f.length(); }

static int l(Object o) {
  return o instanceof String ? l((String) o)
    : l((Collection) o); // incomplete
}




static String fixNewLines(String s) {
  return s.replace("\r\n", "\n").replace("\r", "\n");
}
static volatile boolean ping_pauseAll;
static int ping_sleep = 100; // poll pauseAll flag every 100
static volatile boolean ping_anyActions;
static Map<Thread, Object> ping_actions = synchroMap(new WeakHashMap());

// returns true if it did anything
static boolean ping() { try {
  if (ping_pauseAll && !isAWTThread()) {
    do
      Thread.sleep(ping_sleep);
    while (ping_pauseAll);
    return true;
  }
  
  if (ping_anyActions) {
    Object action;
    synchronized(mc()) {
      action = ping_actions.get(currentThread());
      if (action instanceof Runnable)
        ping_actions.remove(currentThread());
      if (ping_actions.isEmpty()) ping_anyActions = false;
    }
    
    if (action instanceof Runnable)
      ((Runnable) action).run();
    else if (eq(action, "cancelled"))
      throw fail("Thread cancelled.");
  }
  
  return false;
} catch (Exception __e) { throw rethrow(__e); } }
static Object callF(Object f, Object... args) {
  return callFunction(f, args);
}
static String unnull(String s) {
  return s == null ? "" : s;
}

static <A> List<A> unnull(List<A> l) {
  return l == null ? emptyList() : l;
}

static <A> Iterable<A> unnull(Iterable<A> i) {
  return i == null ? emptyList() : i;
}

static Object[] unnull(Object[] a) {
  return a == null ? new Object[0] : a;
}

static BitSet unnull(BitSet b) {
  return b == null ? new BitSet() : b;
}
static boolean isFalse(Object o) {
  return eq(false, o);
}
static <A> ArrayList<A> asList(A[] a) {
  return new ArrayList<A>(Arrays.asList(a));
}

static ArrayList<Integer> asList(int[] a) {
  ArrayList<Integer> l = new ArrayList();
  for (int i : a) l.add(i);
  return l;
}

static <A> ArrayList<A> asList(Iterable<A> s) {
  if (s instanceof ArrayList) return (ArrayList) s;
  ArrayList l = new ArrayList();
  if (s != null)
    for (A a : s)
      l.add(a);
  return l;
}

static <A> ArrayList<A> asList(Enumeration<A> e) {
  ArrayList l = new ArrayList();
  if (e != null)
    while (e.hasMoreElements())
      l.add(e.nextElement());
  return l;
}
static String str(Object o) {
  return String.valueOf(o);
}

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


static Map synchroMap() {
  return synchroHashMap();
}

static <A, B> Map<A, B> synchroMap(Map<A, B> map) {
  return Collections.synchronizedMap(map);
}
static Thread currentThread() {
  return Thread.currentThread();
}
static Object callFunction(Object f, Object... args) {
  if (f == null) return null;
  if (f instanceof Runnable) {
    ((Runnable) f).run();
    return null;
  } else if (f instanceof String)
    return call(mc(), (String) f, args);
  else
    return call(f, "get", args);
  //else throw fail("Can't call a " + getClassName(f));
}
static boolean eq(Object a, Object b) {
  if (a == null) return b == null;
  if (a.equals(b)) return true;
  if (a instanceof BigInteger) {
    if (b instanceof Integer) return a.equals(BigInteger.valueOf((Integer) b));
    if (b instanceof Long) return a.equals(BigInteger.valueOf((Long) b));
  }
  return false;
}
  static RuntimeException fail() {
    throw new RuntimeException("fail");
  }
  
  static RuntimeException fail(Throwable e) {
    throw asRuntimeException(e);
  }
  
  static RuntimeException fail(Object msg) {
    throw new RuntimeException(String.valueOf(msg));
  }
  
  static RuntimeException fail(String msg) {
    throw new RuntimeException(unnull(msg));
  }
   
  static RuntimeException fail(String msg, Throwable innerException) {
    throw new RuntimeException(msg, innerException);
  }
  
  // disabled for now to shorten some programs 
  /*static RuntimeException fail(S msg, O... args) {
    throw new RuntimeException(format(msg, args));
  }*/
static List emptyList() {
  return new ArrayList();
  //ret Collections.emptyList();
}
static Object mc() {
  return getMainClass();
}
static boolean isAWTThread() {
  if (isAndroid()) return false;
  if (isHeadless()) return false;
  return isTrue(callOpt(getClass("javax.swing.SwingUtilities"), "isEventDispatchThread"));
}


static Class<?> getClass(String name) {
  try {
    return Class.forName(name);
  } catch (ClassNotFoundException e) {
    return null;
  }
}

static Class getClass(Object o) {
  return o instanceof Class ? (Class) o : o.getClass();
}

static Class getClass(Object realm, String name) { try {
  try {
    return getClass(realm).getClassLoader().loadClass(classNameToVM(name));
  } catch (ClassNotFoundException e) {
    return null;
  }
} catch (Exception __e) { throw rethrow(__e); } }
static Boolean isHeadless_cache;

static boolean isHeadless() {
  if (isHeadless_cache != null) return isHeadless_cache;
  if (GraphicsEnvironment.isHeadless()) return isHeadless_cache = true;
  
  // Also check if AWT actually works.
  // If DISPLAY variable is set but no X server up, this will notice.
  
  try {
    callOpt(getClass("javax.swing.SwingUtilities"), "isEventDispatchThread");
    return isHeadless_cache = false;
  } catch (Throwable e) { return isHeadless_cache = true; }
}
static Object callOpt(Object o) {
  if (o == null) return null;
  return callF(o);
}

static Object callOpt(Object o, String method, Object... args) {
  try {
    if (o == null) return null;
    if (o instanceof Class) {
      Method m = callOpt_findStaticMethod((Class) o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(null, args);
    } else {
      Method m = callOpt_findMethod(o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(o, args);
    }
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Method callOpt_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
  Class _c = c;
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (!m.getName().equals(method)) {
        if (debug) System.out.println("Method name mismatch: " + method);
        continue;
      }

      if ((m.getModifiers() & Modifier.STATIC) == 0 || !callOpt_checkArgs(m, args, debug))
        continue;

      return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

static Method callOpt_findMethod(Object o, String method, Object[] args, boolean debug) {
  Class c = o.getClass();
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (m.getName().equals(method) && callOpt_checkArgs(m, args, debug))
        return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

private static boolean callOpt_checkArgs(Method m, Object[] args, boolean debug) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != args.length) {
    if (debug)
      System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
    return false;
  }
  for (int i = 0; i < types.length; i++)
    if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
      if (debug)
        System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
      return false;
    }
  return true;
}


static RuntimeException asRuntimeException(Throwable t) {
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static Class getMainClass() {
  return main.class;
}

static Class getMainClass(Object o) { try {
  return (o instanceof Class ? (Class) o : o.getClass()).getClassLoader().loadClass("main");
} catch (Exception __e) { throw rethrow(__e); } }
  static Object call(Object o) {
    return callFunction(o);
  }
  
  // varargs assignment fixer for a single string array argument
  static Object call(Object o, String method, String[] arg) {
    return call(o, method, new Object[] {arg});
  }
  
  static Object call(Object o, String method, Object... args) {
    try {
      if (o instanceof Class) {
        Method m = call_findStaticMethod((Class) o, method, args, false);
        m.setAccessible(true);
        return m.invoke(null, args);
      } else {
        Method m = call_findMethod(o, method, args, false);
        m.setAccessible(true);
        return m.invoke(o, args);
      }
    } catch (Exception e) {
      throw e instanceof RuntimeException ? (RuntimeException) e : new RuntimeException(e);
    }
  }

  static Method call_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
    Class _c = c;
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (!m.getName().equals(method)) {
          if (debug) System.out.println("Method name mismatch: " + method);
          continue;
        }

        if ((m.getModifiers() & Modifier.STATIC) == 0 || !call_checkArgs(m, args, debug))
          continue;

        return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (static) with " + args.length + " parameter(s) not found in " + _c.getName());
  }

  static Method call_findMethod(Object o, String method, Object[] args, boolean debug) {
    Class c = o.getClass();
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (m.getName().equals(method) && call_checkArgs(m, args, debug))
          return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (non-static) with " + args.length + " parameter(s) not found in " + o.getClass().getName());
  }

  private static boolean call_checkArgs(Method m, Object[] args, boolean debug) {
    Class<?>[] types = m.getParameterTypes();
    if (types.length != args.length) {
      if (debug)
        System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
      return false;
    }
    for (int i = 0; i < types.length; i++)
      if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
        if (debug)
          System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
        return false;
      }
    return true;
  }


// hmm, this shouldn't call functions really. That was just
// for coroutines.
static boolean isTrue(Object o) {
  if (o instanceof Boolean)
    return ((Boolean) o).booleanValue();
  if (o == null) return false;
  return ((Boolean) callF(o)).booleanValue();
}

static boolean isTrue(Object pred, Object arg) {
  return booleanValue(callF(pred, arg));
}
static Map synchroHashMap() {
  return Collections.synchronizedMap(new HashMap());
}

static int isAndroid_flag;

static boolean isAndroid() {
  if (isAndroid_flag == 0)
    isAndroid_flag = System.getProperty("java.vendor").toLowerCase().indexOf("android") >= 0 ? 1 : -1;
  return isAndroid_flag > 0;
}



// extended over Class.isInstance() to handle primitive types
static boolean isInstanceX(Class type, Object arg) {
  if (type == boolean.class) return arg instanceof Boolean;
  if (type == int.class) return arg instanceof Integer;
  if (type == long.class) return arg instanceof Long;
  if (type == float.class) return arg instanceof Float;
  if (type == short.class) return arg instanceof Short;
  if (type == char.class) return arg instanceof Character;
  if (type == byte.class) return arg instanceof Byte;
  if (type == double.class) return arg instanceof Double;
  return type.isInstance(arg);
}
static String classNameToVM(String name) {
  return name.replace(".", "$");
}
static boolean booleanValue(Object o) {
  return eq(true, o);
}


static RuntimeException rethrow(Throwable e) {
  throw asRuntimeException(e);
}

}