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 int
	fmt.Scan(&n)
	ans := n - 1
	mp := map[int]bool{}
	for i := 2; i <= 1000000; i++ {
		v := n/i - 1
		if n/v == n%v {
			if mp[v] {
				continue
			}
			mp[v] = true
			ans += v
		}
	}
	fmt.Println(ans)
}