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 powersOfNAsHex(int n) { return new InfiniteItIt() { 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 extends IterableIterator implements Infinite {} static interface Infinite {} // you still need to implement hasNext() and next() static abstract class IterableIterator implements Iterator, Iterable { public Iterator iterator() { return this; } public void remove() { unsupportedOperation(); } } static Iterator iterator(Iterable c) { return c == null ? emptyIterator() : c.iterator(); } static UnsupportedOperationException unsupportedOperation() { throw new UnsupportedOperationException(); } static Iterator emptyIterator() { return Collections.emptyIterator(); } }