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)


# coding: utf-8

# In[10]:

import sys
#import math
#input = sys.stdin.readline
N = int(input())


# In[13]:

sum_ = 0
#print(math.sqrt(N))
#print(int(math.sqrt(N)))
#print(int(N**0.5))
rn = N**0.5
if rn%1 == 0:
    rn -= 1
for i in range(1, int(rn)+1):
    if N%i == 0 and i < N//i-1:
        #print(i)
        #print(N/i-1)
        sum_ += N/i-1
print(int(sum_))


# In[ ]: