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.Collections.Generic;
using System.Linq;

public class Prog
{
    public void run()
    {
        int N = int.Parse(Console.ReadLine());
        var input = Console.ReadLine().Split();
        int[] P = Array.ConvertAll(input, int.Parse);
        int First = 0;
        int Sec = 0;
        int ans = 0;
        for(int i = 0; i < N-1; i++)
        {
            First = Math.Max(P[i], P[i + 1]);
            Sec = Math.Min(P[i], P[i + 1]);
            ans += Sec;
            for(int j = i + 2; j < N; j++)
            {
                if(P[j] < Sec)
                {
                    ans += Sec;
                }else if(P[j] < First)
                {
                    Sec = P[j];
                    ans += Sec;
                }
                else
                {
                    Sec = First;
                    First = P[j];
                    ans += Sec;
                }
            }
        }
        Console.WriteLine(ans);
    }
    public static void Main()
    {
        var prog = new Prog();
        prog.run();
    }
    /*
    最小公倍数
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    // ユークリッドの互除法 
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
    */
    //a<=c, b<=d;
}

//Array.ConvertAll(int.Parse)
//str.IndexOf("Stage",System.StringComparison.CurrentCulture)