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 Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

import Text.Printf

main :: IO()
main = do
  s <- readLn
  printf "%s" $ slv s

slv :: Integer -> String
slv s = unwords [show 0, show a, show b, show 0, show a, show (a+b)]
  where (a, b) = searchVal s (mySqrt s)

mySqrt :: Integer -> Integer
mySqrt x = until done improve x
            where done y = (y^2 <= x) && (x < (y+1)^2)  
                  improve y = div (y + (div x y)) 2

searchVal :: Integer -> Integer -> (Integer, Integer)
searchVal s a | a * a + b * b == s = (a, b)
              | otherwise = searchVal s (a-1)
  where b = mySqrt (s - a * a)