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: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-}

import qualified Data.IntMap.Strict as IM
import Data.List

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

solve :: Int -> Int
solve n = sum [ m | m <- pred <$> divisors n, m > 0, let (q, r) = n `divMod` m, q == r ]

divisors :: Int -> [Int]
divisors = go [1] . factorize
  where
    go !xs !mp = case IM.minViewWithKey mp of
      Nothing            -> xs
      Just ((k, v), mp') -> go xs' mp'
        where
          !xs' = (*) <$> xs <*> take (v + 1) (iterate (* k) 1)

factorize :: Int -> IM.IntMap Int
factorize = go 2 IM.empty
  where
    go !k !mp !n
      | k > n     = mp
      | r == 0    = go k mp1 q
      | otherwise = go (k + 1) mp n
      where
        !(q, r) = n `divMod` k
        !mp1    = IM.insertWith (+) k 1 mp