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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

PROGRAM ATCODER

implicit none
integer(16) :: n,i,s_n,ans=0

read*, n

s_n = ceiling(sqrt(real(n,8)),16)

do i = 1, s_n, 1
  if ( mod(n,i) == 0 ) then
    if ( i /= 1 ) then
      if ( mod(n,i-1) == n/(i-1) ) then
        ans = ans + (i-1)
      end if
    end if
    if ( n/i /= 1 ) then
      if ( mod(n,n/i-1) == n/(n/i-1) ) then
        ans = ans + (n/i-1)
      end if
    end if
  end if
end do

print'(i0)', ans

END PROGRAM ATCODER