Problem:
Score : 400 points

Problem Statement

Given is an integer S.
Find a combination of six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfies all of the following conditions:

0 \leq X_1,Y_1,X_2,Y_2,X_3,Y_3 \leq 10^9

The area of the triangle in a two-dimensional plane whose vertices are (X_1,Y_1),(X_2,Y_2), and (X_3,Y_3) is S/2.

We can prove that there always exist six integers that satisfy the conditions under the constraints of this problem.

Constraints

1 \leq S \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

S

Output

Print six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between.
If multiple solutions exist, any of them will be accepted.

Sample Input 1

3

Sample Output 1

1 0 2 2 0 1

The area of the triangle in a two-dimensional plane whose vertices are (1,0),(2,2), and (0,1) is 3/2.
Printing 3 0 3 1 0 1 or 1 0 0 1 2 2 will also be accepted.

Sample Input 2

100

Sample Output 2

0 0 10 0 0 10

Sample Input 3

311114770564041497

Sample Output 3

314159265 358979323 846264338 327950288 419716939 937510582

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let () =
    let main n =
        let s = n in
        let x1 = 0 in
        let y1 = 0 in
        let sq = int_of_float (ceil (sqrt (float (s)))) in
        let rec loop offs =
            let x2 = sq + offs in
            let y3 = sq - offs in
            let sq2 = x2 * y3 - s in
            if x2 > 1_000_000_000 || sq2 < 0 then failwith "??" else
                let rec loop_2 sq3 count =
                    if count > 1000000 || sq3 < 1 then loop (offs + 1) else
                    if sq2 mod sq3 = 0 then
                        let x3 = sq3 in
                        let y2 = sq2 / sq3 in
                        x1, y1, x2, y2, x3, y3
                    else loop_2 (sq3 - 1) (count + 1)
                in
                if sq2 = 0 then x1, y1, x2, 0, 0, y3 else
                let sq3 = int_of_float (floor (sqrt (float (sq2)))) in
                loop_2 sq3 0
        in
        loop 0
    in
    let x1, y1, x2, y2, x3, y3 = main (int_of_string (read_line ())) in
    Printf.printf "%d %d %d %d %d %d\n" x1 y1 x2 y2 x3 y3