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 <A> List<A> lazyListFromIterator(Iterator<A> it) {
  return new RandomAccessAbstractList<A>() {
    List<A> list = new ArrayList();
    
    public int size() { realizeFully(); return list.size(); }
    public A get(int i) { realizeUpTo(i); return list.get(i); }
    
    void realizeUpTo(int i) {
      while (i >= list.size() && it.hasNext())
        list.add(it.next());
    }
    
    void realizeFully() {
      realizeUpTo(Integer.MAX_VALUE);
    }
  };
}
abstract static class RandomAccessAbstractList<A> extends AbstractList<A> implements RandomAccess {
}
}