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 Python (3.4.3) (judge verdict: Accepted)

import math
s = int(input())
root = math.ceil(s**0.5)
#print("root",root)
diff = abs(root**2 - s)
#print("diff",diff)
pf=[]
a = 0
b = 0
#print(int(diff**0.5))
if diff != 1:
  if diff == 2:
    a = 1
    b = 2
  elif diff == 3:
    a = 1
    b = 3
  else:
    test = int(diff**0.5)+1
    for i in range(2, test):
      #print("diffloop",diff)
#      if i == 1710:
#        print("1710diff",diff)
#      if i ==25322:
#        print("25322diff",diff%i)
      while diff%i==0:
        pf.append(i)
        diff//=i
#        print("i",i,"diff",diff)
    if diff>1:pf.append(diff)
    for i in range(len(pf)):
      if(i%2==0):
        if a ==0:
          a = 1
        a*=pf[i]
      else:
        if b ==0:
          b = 1
        b*=pf[i]
else:
  a = 1
  b = 1
if a != 0 and b == 0:
  b = 1
if b != 0 and a == 0:
  a = 0
if a > 10**9:
  a /= pf[0]
  b *= pf[0]
if b > 10**9:
  a *= pf[0]
  b /= pf[0]
#print("pf",pf)
if a >= 0 and b >= 0:
  print("0","0",a,root,root,b)
elif a >= 0 and b < 0:
  print("0",-b,a,root-b,root,0)
elif a < 0 and b >= 0:
  print(-a,"0","0",root,root-a,b)
else:
  print(-a,-b,"0",root-b,root-a,"0")