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
ds = N.prime_division

def dig(ds, n = 1, depth = 0)
  if depth < ds.size
    q,d = ds[depth]
    s = 0
    (0..d).each{ |d|
      s += dig(ds, n, depth+1)
      n *= q
    }
    return s
  else
    m = n - 1
    r = N/n
    return r < m ? m : 0
  end
end

p dig(ds)