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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws IOException, Exception{
		BufferedReader st = new BufferedReader(new InputStreamReader(System.in));
		int n = getInt(st);
		int[] data = getIntArry(st);
		int ans = 0;
		for(int l=0;l<n-1;l++) {
			for(int r=l+1;r<n;r++) {
				int max = 0;
				int ne = 0;
				for(int i=l;i<=r;i++) {
					if(max < data[i]) {
						ne = max;
						max = data[i];
					} else if(ne < data[i]) {
						ne = data[i];
					}

				}
				ans+=ne;
			}
		}
		anser(ans);

	}

	private static int getInt(BufferedReader st) throws Exception, IOException {
		int num = Integer.parseInt(st.readLine());
		return num;
	}

	private static int[] getIntArry(BufferedReader st) throws Exception, IOException {
		String line = st.readLine();
		String[] strData = line.split(" ");
		int[] intData = new int[strData.length];
		for (int i = 0; i < strData.length; i++) {
			intData[i] = Integer.parseInt(strData[i]);
		}
		return intData;
	}

	private static void anser(int num) {
		System.out.println(num);
	}
}