Problem:
Score : 500 points

Problem Statement

Snuke received a positive integer N from Takahashi.
A positive integer m is called a favorite number when the following condition is satisfied:

The quotient and remainder of N divided by m are equal, that is, \lfloor \frac{N}{m} \rfloor = N \bmod m holds.

Find all favorite numbers and print the sum of those.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

8

Sample Output 1

10

There are two favorite numbers: 3 and 7. Print the sum of these, 10.

Sample Input 2

1000000000000

Sample Output 2

2499686339916

Watch out for overflow.

Solution in Python (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
from math import sqrt
n = int(input())

selected = set()
res = 0
for w in range(1,int(sqrt(n))+10):
    if n%w==0:
        m = (n-w)//w
        if m>0 and m not in selected and n//m == n%m:
            res += m
            selected.add(m)

        w2 = n//w
        m2 = (n-w2)//w2
        if m2>0 and m2 not in selected and n//m2 == n%m2:
            res += m2
            selected.add(m2)
print(res)