Problem:
Score: 500 points

Problem Statement

Given is a permutation P of \{1, 2, \ldots, N\}.

For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.

Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Constraints

2 \le N \le 10^5

1 \le P_i \le N

P_i \neq P_j (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Sample Input 1

3
2 3 1

Sample Output 1

5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

30

Sample Input 3

8
8 2 7 3 4 5 6 1

Sample Output 3

136

Solution in Julia (0.5.0) (judge verdict: Time Limit Exceeded)

using Base.Collections
using Base.Order

parseInt(x) = parse(Int, x)
parseArray(x::Array{SubString{String}, 1}) = map(parseInt, x)

function main()
  n = readline() |> parseInt
  a = readline() |> split |> parseArray

  f(l,r)=begin
    l>=r && return 0
    ix=sortperm(a[l:r], rev=true)+l-1
    i,j=minmax(ix[1], ix[2])
    a[ix[2]]*(i-l+1)*(r-j+1)+f(l,j-1)+f(i+1,r)-f(i+1,j-1)
  end

  ans = f(1, n)

  println(ans)
end

main()