sclass BWIntegralImage {
  int w, h;
  int[] data; // 1 entry per pixel
  
  *() {}
  
  *(BufferedImage img) { this(BWImage(img)); }
  
  *(BWImage img) {
    w = img.w();
    h = img.h();
    data = new int[w*h];
    int i = 0;
    for y to h: {
      int sum = 0;
      for x to w: {
        sum += img.getByte(x, y) & 0xFF;
        data[i] = y > 0 ? sum + data[i-w] : sum;
        i++;
      }
    }
  }
  
  // pixels outside of image are considered black
  int get(int x, int y) {
    ret x < 0 || y < 0 ? 0 : data[min(y, h-1)*w+min(x, w-1)];
  }
}