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 A
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = Io.Read<int>();
            var Plist = Io.ReadList<int>();

            var output = 0;
            for (var L = 0; L < N - 1; L++)
            {
                var max = Plist[L];
                var second = 0;
                for (var R = L + 1; R < N; R++)
                {
                    if (max < Plist[R])
                    {
                        second = max;
                        max = Plist[R];
                    }
                    else
                    {
                        second = Math.Max(second, Plist[R]);
                    }

                    output += second;
                }
            }

            Io.Write(output.ToString());
        }
    }

    class Io
    {
        public static string Read()
        {
            return Console.ReadLine();
        }

        public static IEnumerable<string> ReadRepeat(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read());
        }

        public static T Read<T>()
        {
            return (T)Convert.ChangeType(Read(), typeof(T));
        }

        public static IEnumerable<T> ReadRepeat<T>(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read<T>());
        }

        public static string[] ReadList(char devide = ' ')
        {
            return Read().Split(devide);
        }

        public static T[] ReadList<T>(char devide = ' ')
        {
            return ReadList(devide)
                .Select(s => (T)Convert.ChangeType(s, typeof(T)))
                .ToArray();
        }

        public static IEnumerable<T[]> ReadListRepeat<T>(int count, char devide = ' ')
        {
            return Enumerable.Range(0, count).Select(_ => ReadList<T>(devide));
        }

        public static void Write(string value)
        {
            Console.WriteLine(value);
        }
    }
}