Problem:
Score : 400 points

Problem Statement

One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

Constraints

1 ≦ N ≦ 200,000

(a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Sample Input 1

3
2 1 3

Sample Output 1

9

Sample Input 2

4
1 3 2 4

Sample Output 2

19

Sample Input 3

8
5 4 8 1 2 6 7 3

Sample Output 3

85

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.IntSet as S
import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import Data.List

solve :: Int -> S.IntSet -> [(Int, Int)] -> Int
solve _ _ [] = 0
solve n s ((i, x):is) = (i-l)*(r-i)*x + solve n (i `S.insert` s) is
  where
    l = fromMaybe 0 $ S.lookupLT i s
    r = fromMaybe (n+1) $ S.lookupGT i s

main :: IO ()
main = do
  n <- readLn
  a <- sortOn snd . zip [1..] . map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
  print $ solve n S.empty a