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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func Scanner() string {
	sc.Scan()
	return sc.Text()
}

func intScanner() int {
	n, _ := strconv.Atoi(Scanner())
	return n
}

func floatScanner() float64 {
	n, _ := strconv.ParseFloat(Scanner(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func stringSliceScanner(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scanner()
	}
	return a
}
func intSliceScanner(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = intScanner()
	}
	return a
}

var mod int

func main() {
	mod = 1000000007
	buf := make([]byte, 0)
	sc.Buffer(buf, mod)
	sc.Split(bufio.ScanWords)
	n := intScanner()
	ans := 0
	for i := 1; i*i < n; i++ {
		if n%i == 0 {
			if i != 1 {
				if n%(i-1) == n/(i-1) {
					ans += i - 1
				}
			}
			j := n / i
			if n%(j-1) == n/(j-1) {
				ans += j - 1
			}
		}
	}
	fmt.Println(ans)
}