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)

module Main where

import Control.Monad

main :: IO ()
main = do
  n <- readLn :: IO Integer
  print $ n * (n + 1) `div` 2
  
  -- forM_ [1..10] $ \n -> do
  --   let xs = [1..n]
  --   print $ maximum $ map (sum . modOrig xs) $ perm2 xs n

-- modOrig x y = zipWith mod y x


-- perm2 :: Eq a => [a] -> Int -> [[a]]
-- perm2 _ 0 = [[]]
-- perm2 xs n = [x:ys | x <- xs, ys <- perm2 xs (n-1)]