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 PyPy3 (2.4.0) (judge verdict: Accepted)

#!/usr/bin/env pypy3

import math


def solve(n):
    res = 0
    for q in range(1, math.floor(math.sqrt(n)) + 1):
        m1, mo = divmod(n, q)
        if mo != 0 or m1 - q < 2:
            continue
        res += m1 - 1
    return res


def main():
    n = int(input())
    res = solve(n)
    print(res)


if __name__ == "__main__":
    main()