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.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import Debug.Trace

main :: IO ()
main = readLn >>= print . solve

solve :: Int -> Int
solve n = foldl' count 0 [1..s]
    where
        s = truncate . sqrt $ fromIntegral n

        count acc r
            | b == 0 && r < a - 1 = acc + a - 1
            | otherwise = acc
            where
                (a, b) = n `divMod` r

readLine :: IO [Int]
readLine = unfoldr (fmap (second (maybe B.empty snd . B.uncons)) . B.readInt) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine