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)

N = int(input())
sqrtN = int(N ** 0.5)
fac = []
for i in range(1, sqrtN+1):
    if N % i == 0:
        fac.append(i)
        if i ** 2 != N:
            fac.append(N//i)
ans = 0
div = 0
for p in fac[1:]:
    div = p - 1
    if N // div == N % div:
        # print(i, N//i, N%i)
        ans += div
print(ans)