Scanf.scanf "%d" (fun n ->
    let mat = Array.make_matrix n n 0 in

    let rec loop i x y vx vy =
        if i > n * n then () else (
            mat.(y).(x) <- i;
            let x1 = x + vx in
            let y1 = y + vy in
            if x1 < 0 || x1 >= n || y1 < 0 || y1 >= n || mat.(y1).(x1) <> 0 then (
                let vx, vy = -vy, vx in
                loop (i + 1) (x + vx) (y + vy) vx vy
            ) else loop (i + 1) x1 y1 vx vy
        )
    in
    loop 1 0 0 1 0;
    Array.iter (fun v ->
        Array.iter (Printf.printf "%03d ") v;
        print_newline ()
    ) mat
)