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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] A = new int[N];
            string[] A_in = Console.ReadLine().Split(' ');
            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(A_in[i]);
            }
            int result = 0;
            for (int i = 0; i < N-1; i++)
            {
                for (int j = i+1; j < N; j++)
                {
                    result += findX(A, i, j);
                }
            }

            Console.WriteLine(result.ToString());
//            Console.Read();
        }
        static int findX(int[] input, int L, int R)
        {
            int[] subArray = new int[(R - L + 1)];
            Array.Copy(input, L, subArray, 0, (R - L + 1));
            int max = subArray.Max();
            for (int i = 0; i < (R-L+1); i++)
            {
                if (subArray[i] == max) subArray[i] = 0;
            }
            return subArray.Max();
        }
    }
}