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: Wrong Answer)

-- diverta 2019 D problem
import Control.Monad
import qualified Data.Text as T

-- conversion from String to Int
toInt :: String -> Int
toInt x = read x :: Int

-- obtain [Int] from I/O
getInts :: IO [Int]
getInts = do
  x <- getLine
  let y = (map $ toInt) $ words x
  return y
  
div_half :: Integer -> [Integer]
div_half n = [m | m <- [1..(ceiling(sqrt(fromIntegral n)))], (mod n m == 0)]

div_all :: Integer -> [Integer]
div_all n = (div_half n) ++ [(div n m) | m <- (div_half n), not (m*m == n)]

-- calculation of answer
proD :: Integer -> [Integer]-> Integer
proD n [] = 0
proD n (x:xs) = 
  if x == 1 || x == 2 then (proD n xs)
  else
    if (mod n (x-1)) /= 0 then (x-1)+(proD n xs)
    else (proD n xs)

-- main function
main :: IO ()
main = do
  n1 <- getInts
  let n = toInteger (head n1)
  print (proD n (div_all n))