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 long gzippedSize(byte[] data) { try {
  JustCountingOutputStream jcos = new JustCountingOutputStream();
  GZIPOutputStream gos = new GZIPOutputStream(jcos);
  gos.write(data, 0, l(data));
  gos.close();
  return jcos.get();
} catch (Exception __e) { throw rethrow(__e); } }

static int gzippedSize(String s) {
  return l(gzipString(s));
}

static long gzippedSize(File f) { try {
  JustCountingOutputStream jcos = new JustCountingOutputStream();
  var gos = new GZIPOutputStream(jcos);
  file2stream(f, gos);
  gos.close();
  return jcos.get();
} catch (Exception __e) { throw rethrow(__e); } }
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 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 byte[] gzipString(String s) { try {
  ByteArrayOutputStream baos = new ByteArrayOutputStream();
  GZIPOutputStream gos = new GZIPOutputStream(baos);
  OutputStreamWriter outputStreamWriter = new OutputStreamWriter(gos, "UTF-8");
  PrintWriter printWriter = new PrintWriter(outputStreamWriter);
  printWriter.print(s);
  printWriter.close();
  gos.close();
  return baos.toByteArray();
} catch (Exception __e) { throw rethrow(__e); } }


static void file2stream(File src, OutputStream out) throws IOException {
  FileInputStream inputStream = new FileInputStream(src);
  try {
    copyStream(inputStream, out);
  } finally {
    inputStream.close();
  }
}




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


static void copyStream(InputStream in, OutputStream out) { try {
  byte[] buf = new byte[65536];
  while (true) {
    int n = in.read(buf);
    if (n <= 0) return;
    out.write(buf, 0, n);
  }
} catch (Exception __e) { throw rethrow(__e); } }




static class JustCountingOutputStream extends OutputStream {
  long counter;
  
  @Override
  public void write(int b) throws IOException {
    ++counter;
  }

  @Override
  public void write(byte[] b) throws IOException {
    counter += b.length;
  }

  @Override
  public void write(byte[] b, int off, int len) throws IOException {
    counter += len;
  }
  
  final long get(){ return getFilePointer(); }
long getFilePointer() { return counter; }
}

}