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 Integer[] intArrayToBoxed(int[] l) {
  if (l == null) return null;
  int n = l.length;
  Integer[] a = new Integer[n];
  for (int i = 0; i < n; i++)
    a[i] = l[i];
  return a;
}

static Integer[] intArrayToBoxed(int[] l, int from, int to) {
  if (l == null) return null;
  Integer[] a = new Integer[to-from];
  for (int i = from; i < to; i++)
    a[i-from] = l[i];
  return a;
}}