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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main{
    public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);

      int n = Integer.parseInt(sc.next());

      int[] p = new int[n];

      for(int i=0;i<n;i++){
        p[i] = Integer.parseInt(sc.next());
      }

      int[] aaa = new int[n];

      int ans = 0;

      for(int i=0;i<n-1;i++){
        for(int j=1;j<n;j++){
          for(int k=i;k<=j;k++){
            aaa[k]=p[k];
          }
          Arrays.sort(aaa);
          ans += aaa[n-2];
          aaa = new int[n];
        }
      }
      System.out.println(ans);

    }
}