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: Time Limit Exceeded)

import Data.List
import Data.Maybe
import qualified Data.IntSet as S

type Index = Int
type Memo = S.IntSet

data Props = Props { total :: Integer, memo :: Memo } deriving Show

step :: Props -> (Integer, Index) -> Props
step props (x, i) = -- traceShow (props, x, i)
  Props total' memo'
  where
    Props total memo = props
    h = fromIntegral $ fromJust (S.lookupGT i memo) - i
    w = fromIntegral $ i - fromJust (S.lookupLT i memo)
    total' = total + x * h * w
    memo' = S.insert i memo

solve :: [Integer] -> Integer
solve l = total result
  where
    n = length l
    l' = sort $ zip l [1..]
    props = Props 0 (S.fromList [0, n + 1])
    result = foldl' step props l'

main = getContents >>= print . solve . map read . words . last . lines