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 javax.imageio.*;
import java.math.*;
// out of full long range (including negative values)
class main {

static long randomLong() {
  return defaultRandomGenerator().nextLong();
}

static long randomLong(Random random) {
  return random.nextLong();
}

// returns number between 0 and max-1
static long randomLong(long max) { return randomLong(defaultRandomGenerator(), max); }
static long randomLong(Random random, long max) {
  return mod(randomLong(random), max);
}

// min <= value < max
static long random(long min, long max) {
  return min+randomLong(max-min);
}
static Random defaultRandomGenerator() {
  return ThreadLocalRandom.current();
}


// better modulo that gives positive numbers always
static int mod(int n, int m) {
  return (n % m + m) % m;
}

static long mod(long n, long m) {
  return (n % m + m) % m;
}

static BigInteger mod(BigInteger n, int m) {
  return n.mod(bigint(m));
}

static double mod(double n, double m) {
  return (n % m + m) % m;
}





static BigInteger bigint(String s) {
  return new BigInteger(s);
}

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



}