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 java.util.function.*;
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 java.awt.geom.*;
import javax.imageio.*;
import java.math.*;
class main {

static IterableIterator<Integer> lineStartIndexesIterator(String s) {
  return new IterableIterator<Integer>() {
    int i;
    
    public boolean hasNext() {
      return i >= 0;
    }
    
    public Integer next() {
      int j = i;
      i = indexOf(s, '\n', i);
      if (i >= 0) ++i;
      return j;
    }
  };
}
static <A> int indexOf(List<A> l, A a, int startIndex) {
  if (l == null) return -1;
  int n = l(l);
  for (int i = startIndex; i < n; i++)
    if (eq(l.get(i), a))
      return i;
  return -1;
}

static <A> int indexOf(List<A> l, int startIndex, A a) {
  return indexOf(l, a, startIndex);
}

static <A> int indexOf(List<A> l, A a) {
  if (l == null) return -1;
  return l.indexOf(a);
}

static int indexOf(String a, String b) {
  return a == null || b == null ? -1 : a.indexOf(b);
}

static int indexOf(String a, String b, int i) {
  return a == null || b == null ? -1 : a.indexOf(b, i);
}

static int indexOf(String a, char b) {
  return a == null ? -1 : a.indexOf(b);
}

static int indexOf(String a, int i, char b) {
  return indexOf(a, b, i);
}

static int indexOf(String a, char b, int i) {
  return a == null ? -1 : a.indexOf(b, i);
}

static int indexOf(String a, int i, String b) {
  return a == null || b == null ? -1 : a.indexOf(b, i);
}

static <A> int indexOf(A[] x, A a) {
  int n = l(x);
  for (int i = 0; i < n; i++)
    if (eq(x[i], a))
      return i;
  return -1;
}

static <A> int indexOf(Iterable<A> l, A a) {
  if (l == null) return -1;
  int i = 0;
  for (A x : l) {
    if (eq(x, a))
      return i;
    i++;
  }
  return -1;
}





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(short[] a) { return a == null ? 0 : a.length; }
static int l(long[] 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(double[] 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(Iterator i) { return iteratorCount_int_close(i); } // consumes the iterator && closes it if possible

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






static <A> int iteratorCount_int_close(Iterator<A> i) { try {
  int n = 0;
  if (i != null) while (i.hasNext()) { i.next(); ++n; }
  if (i instanceof AutoCloseable) ((AutoCloseable) i).close();
  return n;
} catch (Exception __e) { throw rethrow(__e); } }


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

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

static String str(char[] c, int offset, int count) {
  return new String(c, offset, count);
}




static RuntimeException rethrow(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  throw t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}

static RuntimeException rethrow(String msg, Throwable t) {
  throw new RuntimeException(msg, t);
}




static void _handleError(Error e) {
  //call(javax(), '_handleError, e);
}




// you still need to implement hasNext() and next()
static abstract class IterableIterator<A> implements Iterator<A>, Iterable<A> {
  public Iterator<A> iterator() {
    return this;
  }
  
  public void remove() {
    unsupportedOperation();
  }
}


static <A> Iterator<A> iterator(Iterable<A> c) {
  return c == null ? emptyIterator() : c.iterator();
}


static UnsupportedOperationException unsupportedOperation() {
  throw new UnsupportedOperationException();
}




static Iterator emptyIterator() {
  return Collections.emptyIterator();
}



}