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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main {

   def main(args: Array[String]): Unit = {
     import scala.io.StdIn._
     val N = readLine().toLong

     val start = Math.floor((1 + Math.sqrt(4 * N + 1))/2).toLong

     def rec(m: Long, acm: Long): Long =
       if (m < N) {
         if ((N / m) == (N % m)) rec(m + 1, acm + m)
         else rec(m + 1, acm)
       } else acm

     println(rec(start, 0))
   }

}