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: Accepted)

require 'prime'

# 約数リスト
def divisors(n)
  n.prime_division.inject([1]) do |array, (k, v)|
    (0..v).map{ |i| k ** i }.product(array).map{ |a, b| a * b }
  end.sort
end

n = gets.to_i
n_divisors = divisors(n)
ans = 0
n_divisors.each do |num|
  tmp = n - num
  next if tmp < 1
  divisor = tmp / num
  ans += divisor if num == n % divisor
end
puts ans