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 Go (1.6) (judge verdict: Runtime Error)

package main

import "fmt"

func main() {
	var N int64
	fmt.Scan(&N)

	var fs []int64
	for i := int64(2); i <= int64(N/2)+1; i++ {
		if N%i == 0 {
			fs = append(fs, i)
		}
	}
	fs = append(fs, N)
	var ret int64
	for _, f := range fs {
		if N/(f-1) == N%(f-1) {
			ret += (f - 1)
		}
	}
	fmt.Println(ret)
}