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.Linq;
using System.Collections.Generic;

public class Program {
  public static void Main() {    
    int N = int.Parse(Console.ReadLine().Trim());
    int[] P = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x)).ToArray();  
    
    long sum = 0;
    
    for(var i = 0; i < N - 1; i++) {
      int max = P[i];
      int secondMax = 0;    
      var stop = false;
      var j = 0;
      for(j = i + 1; j < N; j++) {
        if(P[j] > max) {
          secondMax = max;
          max = P[j];
        } else
        if(P[j] > secondMax) {
          secondMax = P[j];
        }             
        sum += secondMax;
        //Console.WriteLine(secondMax);
        if(max == N && secondMax == N - 1) {
          stop = true;
          break;
        }
      }
      if(stop) {
        //Console.WriteLine(sum);
        sum += (N - 1) * (N - j - 1);        
      }
    }
    Console.WriteLine(sum);
  }
}