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 JavaScript (node.js v5.12) (judge verdict: Accepted)

var lines = [];
var readline = require('readline');

var rl = readline.createInterface({
    input: process.stdin,
    output: process.stdout,
});

rl.on('line', function (x) {
    lines.push(x);
});

rl.on('close', function () {
    var N = Number(lines[0]);
    var ans = 0;

    // mで割った余りがrなので　m > r
    // N = m * r + r > r^2
    // (N-r)/r = m > r

    for (var r = 1; r * r <= N; r++) {
        if ((N - r) % r === 0 && (N - r) / r > r) { ans += (N - r) / r }
    }
    console.log(ans)
});