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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
    val N = readLine()!!.toLong()

    val fact = factors(N)

    println(
        fact.map { it - 1 }
            .filter { it != 0L && N / it == N % it }
            .sum()
    )

//    for (N in 1..200L) {
//        val list = ArrayList<Long>()
//        for (i in 2 until N) {
//            if (N % i == N / i) {
//                list.add(i)
//            }
//        }
//        println("$N: ${list.joinToString(" ")}")
//    }
}

fun factors(n: Long): List<Long> {
    var i = 1L
    val factors = ArrayList<Long>()

    while(i * i <= n) {
        if (n % i == 0L) {
            factors.add(i)

            if (n / i != i) {
                factors.add(n / i)
            }
        }
        i++
    }
    factors.sort()

    return factors
}