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 Ruby (2.3.3) (judge verdict: Accepted)

require 'prime'
def divisors(n)
  n.prime_division.inject([1]) do |ary, (p, e)|
    (0..e).map{ |e1| p ** e1 }.product(ary).map{ |a, b| a * b }
  end.sort
end
#x以下の２数の積になるか？
def div2(n,x)
  div_ls=divisors(n)
  div_len=div_ls.length
  if div_ls[div_len/2]<x
    return [div_ls[div_len/2-1], div_ls[div_len/2]]
  else
    return false
  end
end
S = gets.to_i
N=Math.sqrt(S).ceil
n=N
####S=N^2-abとできればよい
while(1)
  ab=n*n-S
  ###ab=0か？
  if ab==0
    puts [0,0,0,n,n,0].join(' ')
    break
  end
  ab_ls=div2(ab,2*n-1)
  ###abが2n-1以下の2数の積か？
  if ab_ls!=false
    puts [0,0,ab_ls[0],n,n,ab_ls[1]].join(' ') 
    break
  end
  n=n+1
end