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
import qualified Data.ByteString.Char8 as BS
import           Data.Maybe

readInt = fst . fromJust . BS.readInt
getInt = readInt <$> BS.getLine

x `mydiv` y = if y /= 0 then x `div` y else 0
x `mymod` y = if y /= 0 then x `mod` y else 1

main = do
  n <- getInt

  let solve i res | i*i >     n    = res
                  | n `mod` i == 0 = let m1 = i - 1
                                         q1 = n `mydiv` m1
                                         r1 = n `mymod` m1

                                         m2 = n `div` i - 1
                                         q2 = n `mydiv` m2
                                         r2 = n `mymod` m2

                                         res' = res
                                           + (if q1 == r1 then m1 else 0)
                                           + (if q2 == r2 then m2 else 0)
                                     in solve (i+1) res'
                  | otherwise      = solve (i+1) res

  print $ solve 1 0