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: Runtime Error)

import math

m = math.floor(n/2)
if n>2:
    q = int( n / m )
    lm= m
    s = n - 1
else:
    s = 0

while( m>1 ):
    m = math.floor(n/(q+1))
    r0 = n % ( m + 1 )
    if r0>=q:
        d= r0  - q
        if d%q==0:
            s+= ( m+1+int(d/q) )
    #
    # for next
    q = int( n/m )
    lm= m
#
print( s )