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)

import Control.Monad

readIntLine :: IO ([Int])
readIntLine = do
    x <- getLine
    return $ map (read :: String -> Int) $ words x

main :: IO ()
main = do
    [n] <- readIntLine
    print $ solve n

fav n s = div n s == mod n s

canBeRem n k
    | mod n k == 0 && fav n s = s
    | otherwise               = 0
         where s = div (n - k) k

allCands x n
    | x * x >= n = []
    | otherwise  = x:(allCands (x+1) n)

solve n = sum $ map (canBeRem n) $ allCands 1 n