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.Arrays;
import java.util.Scanner;

/**
 * @author author
 *
 */
public class Main {

  /**
   * @param args
   */
  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());
    }

    long x = 0;
    int[] copyArray;
    for (int l = 0; l < n - 1; l++) {
      for (int r = l + 1; r < n; r++) {
        copyArray = Arrays.copyOfRange(P, l, r + 1);
        Arrays.sort(copyArray);
        x += copyArray[copyArray.length - 2];
      }
    }

    System.out.println(x);

  }

}