let count_neighbours (x,y) board size =
  if size < 0 then 0
  else
    let neighbours (x,y) board size =
    match (size-1) with
       size when x=size && y=size -> get_cell (x-1,y) board + get_cell (x-1,y-1) board + get_cell (x,y-1) board
      |size when size=x && y=0 -> get_cell (x-1,y) board + get_cell (x-1,y+1) board + get_cell (x,y-1) board
      |size when size=x -> get_cell (x,y+1) board + get_cell (x-1,y+1) board + get_cell (x-1,y) board +
    get_cell (x-1,y-1) board + get_cell (x,y-1) board
      |size when x=0 && size=y -> get_cell(x+1,y) board + get_cell (x+1,y-1) board + get_cell (x,y-1) board
      |size when x=0 && y=0 -> get_cell (x+1,y) board + get_cell (x+1,y+1) board + get_cell (x,y+1) board
      |size when x=0 -> get_cell (x+1,y+1) board + get_cell (x+1,y) board + get_cell (x,y+1) board +
    get_cell (x-1,y-1) board + get_cell (x-1,y) board
      |size when size=y -> get_cell (x-1,y) board + get_cell (x+1,y) board +get_cell (x+1,y-1) board +
    get_cell (x,y-1) board + get_cell (x-1,y-1) board
      |size when y=0 -> get_cell (x,y+1) board + get_cell (x+1,y+1) board + get_cell (x+1,y) board +
    get_cell (x-1,y) board + get_cell (x-1,y+1) board
      | _ -> get_cell (x-1,y-1) board + get_cell (x-1,y) board + get_cell (x-1,y+1) board +
    get_cell (x,y-1) board + get_cell (x,y+1) board + get_cell (x+1,y-1) board + get_cell (x+1,y) board +
    get_cell (x+1,y+1) board
    in
    neighbours (x,y) board size;;



let seed_life board size nb =
  if nb < 0 then
    invalid_arg "Le nombre de cellule ne peux pas etre nul "
  else
    let rec seed board nb = match nb with
	 | 0 -> board
         | n -> seed (put_cell new_cell (1+ Random.int size ,1+ Random.int size ) board) (n-1)
    in seed board nb ;;

let new_board size nb =
  if size < 0 then
    invalid_arg " The size can't be negatif "
  else seed_life (init_board (size,size) empty) size nb ;;