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)

# https://atcoder.jp/contests/diverta2019/tasks/diverta2019_d
import itertools
from collections import Counter
from collections import defaultdict
import bisect

def main():
    N = int(input())

    ans = 0
    i = 1
    while i * i <= N:
        if N % i == 0:
            opo1 = i - 1
            if opo1 > 0 and N // opo1 == N % opo1:
                ans += opo1
            opo2 = N // i - 1
            if opo2 > 0 and N // opo2 == N % opo2:
                ans += opo2

        i += 1

    print(ans)


if __name__ == '__main__':
    main()