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.*;
import java.time.Duration;
import java.lang.invoke.VarHandle;
import java.lang.invoke.MethodHandles;
class main {

static <A, B> TreeMap<A, B> asRevTreeMap(Map<A, B> map) {
  Comparator<A> comparator = reverseComparator();
  if (isTreeMapWithComparator(map, comparator))
    return (TreeMap) map;
  var m2 = new TreeMap(comparator);
  m2.putAll(map);
  return m2;
}
static <A> Comparator<A> reverseComparator(Comparator<A> c) {
  return (a, b) -> c.compare(b, a);
}

static <A> Comparator<A> reverseComparator() {
  return (a, b) -> cmp(b, a);
}



static <A, B> boolean isTreeMapWithComparator(Map<A, B> map, Comparator<A> comparator) {
  if (map instanceof TreeMap && eq(((TreeMap) map).comparator(), comparator))
    return true;
  return false;
}




static int cmp(Number a, Number b) {
  return a == null ? b == null ? 0 : -1 : cmp(a.doubleValue(), b.doubleValue());
}

static int cmp(double a, double b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(int a, int b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(long a, long b) {
  return a < b ? -1 : a == b ? 0 : 1;
}

static int cmp(Object a, Object b) {
  if (a == null) return b == null ? 0 : -1;
  if (b == null) return 1;
  return ((Comparable) a).compareTo(b);
}


static boolean eq(Object a, Object b) {
  return a == b || a != null && b != null && a.equals(b);
}






static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return c == null ? "null" : new String(c);
}

static String str(char[] c, int offset, int count) {
  return new String(c, offset, count);
}



}