let grid = Array.make_matrix (grid_width + 2) (grid_height + 2) None
let _ =
  grid.(grid_width).(grid_height) <- Some unit_big_int;
  for x = 0 to grid_width + 1 do
    grid.(x).(succ grid_height) <- Some zero_big_int
  done;
  for y = 0 to grid_height do
    grid.(succ grid_width).(y) <- Some zero_big_int
  done