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"
	"strings"
)

func getNextLine(scanner *bufio.Reader) string {
	var buffer string
	for {
		line, isPrefix, _ := scanner.ReadLine()
		buffer += string(line)
		if isPrefix == false {
			break
		}
	}
	return buffer
}

func getIntList(scanner *bufio.Reader) []int {
	list := strings.Split(getNextLine(scanner), " ")
	l := len(list)
	result := make([]int, l)
	for i := 0; i < l; i++ {
		result[i], _ = strconv.Atoi(list[i])
	}
	return result
}

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := bufio.NewReader(fp)

	var n, ans, i int64
	ans = 0

	fmt.Sscan(getNextLine(scanner), &n)

	orgN := n

	divs := make([]int64, 0)

	for i = 1; i*i <= n; i++ {
		if n%i == 0 {
			divs = append(divs, i)
			if n > i*i {
				divs = append(divs, n/i)
			}
		}
	}

	for j := 0; j < len(divs); j++ {
		if divs[j] == 1 {
			continue
		}
		if orgN/(divs[j]-1) == orgN%(divs[j]-1) {
			ans += divs[j] - 1
		}
	}
	fmt.Println(ans)
}