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.Text;
using System.Linq;


class Solver
    {
        /*
         * https://atcoder.jp/contests/abc140/tasks/abc140_e
         * 
         */
        public void Solve()
        {
            var n = u.readInt();
            var P = u.readIntArrayBySplit();
            //Console.WriteLine(P.AsJoinedString());
            var ans = 0;
            for (int L = 0; L < n-1; L++)
            {
                for (int R = L+1; R < n; R++)
                {
                    ans += P.Skip(L).Take(R - L + 1).OrderByDescending(x => x).Skip(1).First();
                    //Console.WriteLine(string.Format("L:{0} R:{1} ans:{2}", L, R, ans));
                }
            }

            Console.WriteLine(ans);
        }
        static void Main()
        {
            var solver = new Solver();
            solver.Solve();
        }
    }
    static class u
    {
        public static void outA(int[] A) { Console.WriteLine(string.Join(" ", A)); }
        static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
        public static int readInt() { return int.Parse(Console.ReadLine()); }
        public static int[] readIntArrayBySplit() { return Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray(); }

    }