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 BufferedImage byteArrayToGrayBufferedImage(byte[] pixels, int w, int h) {
  PixelInterleavedSampleModel sm = new PixelInterleavedSampleModel(
    DataBuffer.TYPE_BYTE,
    w,
    h,
    1, // pixelStride
    w, // scanlineStride,
    new int[] {0} // bandOffsets
  );
  DataBufferByte db = new DataBufferByte(pixels, pixels.length);
  WritableRaster wr = Raster.createWritableRaster(sm, db, new Point());
  return new BufferedImage(grayColorModel(), wr, false, null);
}
static ColorModel grayColorModel_cache;
static ColorModel grayColorModel() { if (grayColorModel_cache == null) grayColorModel_cache = grayColorModel_load(); return grayColorModel_cache; }

static ColorModel grayColorModel_load() {
  return newGrayBufferedImage(1, 1).getColorModel();
}




// undefined color, seems to be all black in practice
static BufferedImage newGrayBufferedImage(int w, int h) {
  return new BufferedImage(w, h, BufferedImage.TYPE_BYTE_GRAY);
}

/*static BufferedImage newGrayBufferedImage(int w, int h, byte[] pixels) {
  ret byteArrayToGrayBufferedImage(pixels, w, h);
}*/



}