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: Runtime Error)

require 'prime'

def _divisors(primes, k)
Enumerator.new do |y|
if primes.size == k
y << 1
else
p, e = primes[k]
_divisors(primes, k + 1).each {|d|
(e + 1).times {|e1|
y << p ** e1 * d
 }
 }
end
end
end

def divisors(n)
 _divisors(Prime.prime_division(n), 0).to_a.sort
end

n=gets.to_i
array=divisors(n)
m=array.length
index=(0...m-1).bsearch {|i| array[i]*(array[i]+1)>=n}
ans2=0
array[0...index].map{|value|
    ans2+=n/value-1
}

puts ans2