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: Accepted)


import qualified Data.ByteString.Char8 as C
import Data.List
import Control.Monad

import qualified Data.IntMap as M
import qualified Data.Sequence as S

import Data.Foldable(toList)
import Data.Maybe(fromMaybe)


r :: IO [Int]
r  = unfoldr (C.readInt . C.dropWhile (==' ')) <$> C.getLine

rp :: IO (Int,Int)
rp  = toTup . unfoldr (C.readInt . C.dropWhile (==' ')) <$> C.getLine
    where toTup [a,b] = (a,b)


main :: IO ()
main = do
    n <- readLn :: IO Int
    print $ div (n*(n-1)) 2