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;

namespace abc140_e
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var pList = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
            var secondMeme = new Dictionary<Tuple<int, int>, int>();

            var sum = 0;
            foreach (var l in GetRange(0, n - 1))
            {
                foreach (var r in GetRange(l + 1, n))
                {
                    var xlr = GetSecond(pList, l, r);
                    sum += xlr;
                }
            }

            Console.WriteLine(sum);
        }

        static int GetSecond(List<int> list, int l, int r)
        {
            var subList = list.GetRange(l, r - l + 1);
            subList.Sort();
            subList.Reverse();
            var count = 0;
            var max2 = -10;

            foreach (var x in subList)
            {
                if (max2 >= 0 && x >= max2)
                {
                    continue;
                }

                count++;
                max2 = x;

                if (count == 2)
                {
                    return max2;
                }
            }

            return max2;
        }

        private static IEnumerable<int> GetRange(int from, int until)
        {
            return Enumerable.Range(from, until - from);
        }
    }
}