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> ArrayList<Integer> intArrayToList(int[] a) {
  if (a == null) return null;
  return intArrayToList(a, 0, a.length);
}

// no range checking on from/to in the interest of S P E E E E E EEED
static <A> ArrayList<Integer> intArrayToList(int[] a, int from, int to) {
  if (a == null) return null;
  ArrayList < Integer > l = new ArrayList<>(to-from);
  for (int i = from; i < to; i++) l.add(a[i]);
  return l;
}}