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)

module Main where

import Data.List
import Control.Monad
import Debug.Trace
import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

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

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as = let
    (fo, la) = span f as
    las = case la of
        [] -> []
        xs -> split f $ tail xs
    in
        case fo of
            [] -> las
            xs -> xs : las
    

main = do
    n <- readInt
    print $  ((n - 1) + 1) * (n - 1) `div` 2