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 rec floor_sqrt acc acc_x_2_x_r sq_acc_minus_z r sq_r =
  if r = 0 then acc
  else
    let sq_acc_minus_z' = sq_acc_minus_z + acc_x_2_x_r + sq_r in
    ( if sq_acc_minus_z' <= 0 then
        floor_sqrt (acc + r) ((acc_x_2_x_r lsr 1) + sq_r) sq_acc_minus_z'
      else
        floor_sqrt acc (acc_x_2_x_r lsr 1) sq_acc_minus_z) (r lsr 1) (sq_r lsr 2)
let floor_sqrt z = floor_sqrt 0 0 (~-z) (1 lsl 30) (1 lsl 60)

let ceil_sqrt n =
  let m = floor_sqrt n in
  if n <= m * m then m else m + 1

let () = Scanf.scanf "%d" @@ fun s ->
  let x1 = ceil_sqrt s in
  Printf.printf "0 0 %d %d 1 %d" x1 (x1 * x1 - s) x1