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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import math

cands=[2*x+3 for x in range( int(10**4.5)+1 )]
primes=[2]
while(1):
    y=cands.pop(0)
    primes.append(y)
    cands=[x for x in cands if x%y!=0]
    if y>cands[-1]**0.5:
        break
primes=primes+cands

S=int(input())
X=math.ceil(S**0.5)
sol=0
if X**2==S:
    print(0,0,X,0,0,X)
else:    
    while(sol==0):
        ab=X**2-S
        cc=[1,1,0]
        t=0
        XX=ab
        for p in primes:
            while( XX%p==0):
                XX//=p
                cc[t]*=p
                if cc[t]>X:
                    t+=1
                    cc[t-1]//=p
                    cc[t]*=p
            if cc[0]>X or cc[1]>X:
                sol=0
                break
            elif XX==1:
                sol=1
                print(0,0,X,cc[0],cc[1],X)
                break
        if sol != 1:
            X+=1