sclass QuadTreeBitMatrix > WidthAndHeightImpl {
  sclass Node {}
  sclass On  > Node {}
  sclass Off > Node {}
  sclass Composite > Node {
    Node a, b, c, d;
  }
  
  *() {}
  *(int *width, int *height) {}
  
  int half(int x) { ret roundUpToPowerOfTwo((x+1)/2); }
  
  Rect rectA(Rect r) { ret rect(r.x, r.y, half(r.w), r.h); }
  Rect rectB(Rect r) { ret rectFromPoints(r.x+half(r.w), r.y, r.x2(), r.y2()); }
  Rect rectC(Rect r) { ret rectFromPoints(r.x, r.y+half(r.h), r.x+half(r.w), r.y2()); }
  Rect rectD(Rect r) { ret rectFromPoints(r.x+half(r.w), r.y+half(r.h), r.x2(), r.y2()); }
}