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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <iostream>
#include <set>
using namespace std;

int main() {
	//受け取り、前処理など
	long N;
	cin >> N;
	vector<pair<long, long>> V(N);
	for (long i = 0; i < N; i++){
		long a;
		cin >> a;
		V.at(i) = make_pair(a, i + 1);
	}
	sort(V.begin(), V.end());
//ペアを受け取り、片方でソート
	//set
	long ans = 0;
	std::multiset<long> S;
	S.insert(0);
	S.insert(0);
	S.insert(N + 1);
	S.insert(N + 1);
	for (long i = 0; i < N; i++){
		long num = V.at(N - 1 - i).second;
		decltype(S)::iterator r = S.lower_bound(num);
		auto s = r;
		s++;
		auto p = r;
		p--;
		p--;
		auto q = r;
		q--; 
		S.insert(num);
		ans += ((*r - num) * (*q - *p) + (*s - *r) * (num - *q)) * (N - i);
	}
	cout << ans << endl;
}