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 IterableIterator<Integer> countBackwardsTo1(int a) {
  return countDownIterator_exclusive(a, 0);
}
static IterableIterator<Integer> countDownIterator_exclusive(int a, int b) {
  return new IterableIterator<Integer>() {
    int i = a;
    
    public boolean hasNext() { return i > b; }
    public Integer next() { return i--; }
  };
}


// 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();
}

}