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: Time Limit Exceeded)

program divertaD
    integer(8) i, N, sum
    read(*, *) N
    sum = 0
    DO 10 i = 1, N
     if (mod(N,i).NE.0) then
      if (((N-mod(N,i))/i).EQ.(mod(N,i))) then
      sum = sum + i
      end if
     end if
    10 continue
    print '(i0)', sum
end program