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: Accepted)

import java.util.*;
public class Main {
	static int N;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		int P[] = new int[N];
		for(int i=0;i<N;i++) P[i]=sc.nextInt()-1;
		sc.close();
		
		//順列の中の大きい数字から見ていきたいので、処理順に配列の添字を入れた配列を用意する
		int idx[] = new int[N]; //添字の数がP配列のどこにあるか
		for(int i=0;i<N;i++) idx[P[i]]=i; 
		
		TreeSet<Integer> ts = new TreeSet<>();
		
		long ans = 0;
		for(int i=N-1;i>=0;i--) {
			int now = idx[i]; //iの場所
			int hi1 = myHigher(ts, now);
			int hi2 = myHigher(ts, hi1);
			int low1 = myLower(ts, now);
			int low2 = myLower(ts, low1);
			
			long cnt =  (long)(hi2-hi1) * (now - low1) + (long)(hi1-now) * (low1 - low2) ;
			ans += cnt * (i+1);
			
			ts.add(now);			
		}
		System.out.println(ans);
	}
	static int myHigher(TreeSet<Integer> ts, int now) {
		if(ts.higher(now)!=null)return ts.higher(now);
		else return N;
	}
	static int myLower(TreeSet<Integer> ts, int now) {
		if(ts.lower(now)!=null)return ts.lower(now);
		else return -1;
	}
	
}