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 IntegerIterator integerIterator(int[] l) {
  return l == null ? null : new IntegerIterator() {
    int i = 0;
    public boolean hasNext() { return i < l.length; }
    public int next() { return l[i++]; }
  };
}
abstract static class IntegerIterator {
  abstract boolean hasNext();
  abstract int next();
}
}