Problem:
Score : 400 points

Problem Statement

For an integer N, we will choose a permutation \{P_1, P_2, ..., P_N\} of \{1, 2, ..., N\}.

Then, for each i=1,2,...,N, let M_i be the remainder when i is divided by P_i.

Find the maximum possible value of M_1 + M_2 + \cdots + M_N.

Constraints

N is an integer satisfying 1 \leq N \leq 10^9.

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum possible value of M_1 + M_2 + \cdots + M_N.

Sample Input 1

2

Sample Output 1

1

When the permutation \{P_1, P_2\} = \{2, 1\} is chosen, M_1 + M_2 = 1 + 0 = 1.

Sample Input 2

13

Sample Output 2

78

Sample Input 3

1

Sample Output 3

0

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import           Control.Monad
import           Data.Array
import qualified Data.ByteString.Char8 as BS
import           Data.List
import           Data.Maybe
import           Data.Ord

readInts :: IO [Int]
readInts = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

main = do
  (n:_) <- readInts
  print $ solve n

solve n = foldl' (+) 0 (zipWith mod nums mods)
  where
    nums = [1 .. n]
    mods = reverse $ 1 : tail nums