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'

n = gets.to_i

class Integer
    def divisor_list
        return [] if self <= 0
        return [1] if self == 1
  
        prime_division.map.with_index { |(base, k), i|
            s = i.zero? ? 0 : 1
            (s..k).map { |n| base ** n }
        }.inject { |res, e| res + res.flat_map { |t| e.map { |v| t * v } } }.sort
    end
end
  
ans = 0
list = n.divisor_list
list.each do |i|
    m = i - 1
    if m != 0
        if n / m == n % m
            ans += m
        end
    end
end

puts ans