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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'prime'
puts gets.to_i.prime_division.to_h.map{|k,v|(v+1).times.map{|mt| k**mt}}.inject([1]){|s,i| s = s.flat_map{|sm| i.map{|im| im * sm }}}.map{|m|m-1}.select{|m|m**2 > $_.to_i}.inject(:+)