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 OCaml (4.02.3) (judge verdict: Accepted)

let n = read_int ()
let i, ans = ref 1, ref 0
let f m = if m > 0 && n / m = n mod m then ans := !ans + m
let _ =
  while !i * !i <= n do if n mod !i = 0 then (f @@ !i - 1; f @@ n / !i - 1); incr i done;
  Printf.printf "%d\n" !ans