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: Wrong Answer)

N = int(input())
ans = 0

for i in range(2, int(N ** 0.5) + 1):
    if N % i == 0:
        m1 = i - 1
        m2 = N // i - 1
        if N // m1 == N % m1:
            ans += m1
        elif m1 != m2 and N // m2 == N % m2:
            ans += m2

ans += N - 1

print(ans)