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: Wrong Answer)

require 'pp'
require 'prime'

s = gets.chomp!.to_i
x = Math.sqrt(s).to_i
y = x

x1 = 0
y1 = 0

primes = Prime.prime_division(s)
sum1 = 1
sum2 = 1
primes.reverse_each do |num, count|
    count.times do |i|
        if sum1 >= sum2
            sum2 *= num
        else
            sum1 *= num
        end
    end
end
x2, y3 = [sum1, sum2].minmax

pp x2
pp y3

if y3 <= 10 ** 9
    puts "0 0 #{x2} 0 0 #{y3}"
else
    sum = 0
    while y3 > 10 ** 9
        if y3 % 2 == 0
            y3 /= 2
            x2 *= 2
            x2, y3 = [y3, x2].minmax
        else
            y3 += 1
            sum += x2
        end
    end

    puts "0 0 #{x2} 1 #{sum} #{y3}" 
end