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())
r = int(n**0.5)
cnt = 0
prime = []
m = n
for i in range(2,r+1):
    while m%i == 0:
        prime.append(i)
        m //= i
if m != 1:
    prime.append(m)
ass = set()
ass.add(1)
for i in range(len(prime)):
    ass2 = set()
    for x in ass:
        if float(x*prime[i]) < n**0.5:
            ass2.add(x*prime[i])
        ass2.add(x)
    ass = ass2
res = 0
for p in ass:
    res += n//p -1
print(res)