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 InfiniteItIt<String> powersOfNAsHex(int n) {
  return new InfiniteItIt<String>() {
    BigInteger i = bigint(1);
    
    public String next() {
      return (i = mul(i, n)).toString(16);
    }
  };
}
static BigInteger bigint(String s) {
  return new BigInteger(s);
}

static BigInteger bigint(long l) {
  return BigInteger.valueOf(l);
}


static BigInteger mul(BigInteger a, BigInteger b) {
  return a.multiply(b);
}

static BigInteger mul(BigInteger a, long b) {
  return a.multiply(bigint(b));
}

static int mul(int a, int b) { return a*b; }




static interface InfiniteItIt<A> extends IterableIterator<A> implements Infinite {}


static interface Infinite {}
// 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();
}



}