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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 140_E
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int P[] = new int[N];

		for(int i=0; i<N; i++) {
			P[i] = sc.nextInt();
		}
		// Scannerクラスのインスタンスをクローズ
		sc.close();

		int l=0, r=0;
		Integer wk[] = null;
		int ret = 0;

		for(l=0; l<N-1; l++) {
			wk = new Integer[N];
			Arrays.fill(wk, 0);

			wk[0] = P[l];
			for(r=l+1; r<N; r++) {
				wk[r-l] = P[r];
				Arrays.sort(wk, Collections.reverseOrder());
				ret += wk[1];
			}
		}

		System.out.println(ret);
	}
}