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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

solve :: Int -> Int
solve n = foldl (+) 0 $ filter (\x -> x > 0 && n `div` x == n `mod` x) [ n `div` c - 1 | c <- (takeWhile (\x -> x * x <= n) [1..]), n `mod` c == 0 ]

main :: IO ()
main = do
  n <- readLn :: IO Int
  print $ solve n