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 String shortClassName2(Object o) {
  if (o == null) return null;
  Class c = o.getClass();
  String name = c.getName();
  return shortenClassName(name);
}
static String shortenClassName(String name) {
  if (name == null) return null;
  int i = lastIndexOf(name, "$");
  if (i < 0) i = lastIndexOf(name, ".");
  return i < 0 ? name : substring(name, i+1);
}




static int lastIndexOf(String a, String b) {
  return a == null || b == null ? -1 : a.lastIndexOf(b);
}

static int lastIndexOf(String a, char b) {
  return a == null ? -1 : a.lastIndexOf(b);
}

// starts searching from i-1
static <A> int lastIndexOf(List<A> l, int i, A a) {
  if (l == null) return -1;
  for (i = min(l(l), i)-1; i >= 0; i--)
    if (eq(l.get(i), a))
      return i;
  return -1;
}

static <A> int lastIndexOf(List<A> l, A a) {
  if (l == null) return -1;
  for (int i = l(l)-1; i >= 0; i--)
    if (eq(l.get(i), a))
      return i;
  return -1;
}


static String substring(String s, int x) {
  return substring(s, x, strL(s));
}

static String substring(String s, int x, int y) {
  if (s == null) return null;
  if (x < 0) x = 0;
  int n = s.length();
  if (y < x) y = x;
  if (y > n) y = n;
  if (x >= y) return "";
  return s.substring(x, y);
}



// convenience method for quickly dropping a prefix
static String substring(String s, CharSequence l) {
  return substring(s, lCharSequence(l));
}




static int min(int a, int b) {
  return Math.min(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }

static double min(double a, double b) {
  return Math.min(a, b);
}

static double min(double[] c) {
  double x = Double.MAX_VALUE;
  for (double d : c) x = Math.min(x, d);
  return x;
}

static float min(float[] c) {
  float x = Float.MAX_VALUE;
  for (float d : c) x = Math.min(x, d);
  return x;
}

static byte min(byte[] c) {
  byte x = 127;
  for (byte d : c) if (d < x) x = d;
  return x;
}

static short min(short[] c) {
  short x = 0x7FFF;
  for (short d : c) if (d < x) x = d;
  return x;
}

static int min(int[] c) {
  int x = Integer.MAX_VALUE;
  for (int d : c) if (d < x) x = d;
  return x;
}


static int l(Object[] a) { return a == null ? 0 : a.length; }
static int l(boolean[] a) { return a == null ? 0 : a.length; }
static int l(byte[] a) { return a == null ? 0 : a.length; }
static int l(short[] a) { return a == null ? 0 : a.length; }
static int l(long[] a) { return a == null ? 0 : a.length; }
static int l(int[] a) { return a == null ? 0 : a.length; }
static int l(float[] a) { return a == null ? 0 : a.length; }
static int l(double[] a) { return a == null ? 0 : a.length; }
static int l(char[] a) { return a == null ? 0 : a.length; }
static int l(Collection c) { return c == null ? 0 : c.size(); }

static int l(Iterator i) { return iteratorCount_int_close(i); } // consumes the iterator && closes it if possible

static int l(Map m) { return m == null ? 0 : m.size(); }
static int l(CharSequence s) { return s == null ? 0 : s.length(); }
static long l(File f) { return f == null ? 0 : f.length(); }



























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




static int strL(String s) {
  return s == null ? 0 : s.length();
}


static int lCharSequence(CharSequence s) {
  return s == null ? 0 : s.length();
}




static <A> int iteratorCount_int_close(Iterator<A> i) { try {
  int n = 0;
  if (i != null) while (i.hasNext()) { i.next(); ++n; }
  if (i instanceof AutoCloseable) ((AutoCloseable) i).close();
  return n;
} catch (Exception __e) { throw rethrow(__e); } }


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);
}




static RuntimeException rethrow(Throwable t) {
  
  if (t instanceof Error)
    _handleError((Error) t);
  
  throw t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}

static RuntimeException rethrow(String msg, Throwable t) {
  throw new RuntimeException(msg, t);
}




static void _handleError(Error e) {
  //call(javax(), '_handleError, e);
}



}