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;

namespace testes
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] str = Console.ReadLine().Split(' ');
            int[] P = new int[N];
            for (int i = 0; i < N; i++) P[i] = int.Parse(str[i]);

            int ans = 0;
            for(int i = 0; i < N-1; i++)
            {
                for(int j = i+1; j < N; j++)
                {
                    ans += functionX(i, j, P);
                }
            }

            Console.WriteLine(ans);


        }
        
        public static int functionX(int L, int R, int[] array)
        {
            int len = R - L + 1;
            int max = 0;
            int max2 = 0;
            for(int i = 0; i < len; i++)
            {
                if (max <= array[L + i])
                {
                    max2 = max;
                    max = array[L + i];
                }
                else if(max2 <= array[L + i]) max2 = array[L + i];
            }
            return max2;
        }
        public static void Rotation(char[] array, int l, int r)
        {
           
            
        }
        
    }

    
}

/*
int a, b, c;
a = int.Parse(Console.ReadLine()); //標準入力
string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
b = int.Parse(str[0]);  //数値で受け取りたい場合は変換する
c = int.Parse(str[1]);
string S = Console.ReadLine();
char[] C = new char[N];
C = S.ToCharArray();
Console.Write("改行なし a = {0} b = {1} c = {2}", a, b, c)//改行なし出力
Console.WriteLine("改行あり a = {0} b = {1} c = {2}", a, b, c);//改行付き出力

string[] str = Console.ReadLine().Split(' ');
int[] a = new int[N];
for(int i = 0; i < N; i++) a[i] = int.Parse(str[i]);
 */