sclass ManyCirclePainter {
  int w, h;
  new L<Circle> circles;
  int[] pixels;

  L<Circle>[] startCircle, stopCircle;
  
  srecord Circle(Pt center, int radius) {}

  run {
    pixels = new int[w*h];
    if (pixels.length == 0) ret;
    int nCircles = l(circles);
    
    startCircle = new L[h];
    stopCircle = new L[h];
    for (circle : circles) {
      int y1 = max(0, circle.center.y-circle.radius);
      int y2 = circle.center.y+circle.radius+1;
      if (y1 >= y2) continue;
      startCircle[y1] = addOrCreate(startCircle[y1], circle);
      if (y2 < h)
        stopCircle[y2] = addOrCreate(stopCircle[y2], circle);
    }
    
    int[] startStop = new[w];
    new Set<Circle> liveCircles;
    int iPixel = 0;
    
    for y to h: {
      fillArray(startStop, 0);
      addAll(liveCircles, startCircle[y]);
      removeAll(liveCircles, stopCircle[y]);
      for (c : liveCircles) {
        // width of circle at this line
        int width = iround(sqrt(sqr(c.radius)-sqr(y-c.center.y)));
        int x1 = c.center.x-width, x2 = c.center.x+width+1;
        if (x1 > w || x2 <= 0) continue; // not visible at all at this row
        startStop[max(x1, 0)]++;
        if (x2 < w)
          startStop[x2]--;
      }
      
      int count = 0;
      for x to w: {
        count += startStop[x];
        pixels[iPixel++] = countToColor(count, nCircles);
      }
    }
  }
  
  int countToColor(int count, int nCircles) {
    ret rgbIntFromBrightness(count/16.0);
  }
}