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: Wrong Answer)

#include <iostream>
#include <map>
#include <set>
using namespace std;

typedef long long ll;

int main() {
	int n;
	cin >> n;

	map<int, int> idx_map;
	for (int i = 0; i < n; i ++) {
		int p;
		cin >> p;
		idx_map[p] = i;
	}

	multiset<int> shown;
	shown.insert(-1);
	shown.insert(-1);
	shown.insert(n);
	shown.insert(n);
	multiset<int>::iterator itr, itr2;
	int l1, l2, u1, u2;
	ll sum = 0;
	for (int p = n; p >= 1; p --) {
		int i = idx_map[p];
		itr = shown.upper_bound(i);
		itr2 = itr;
		u1 = *itr;
		++itr;
		u2 = *(itr);
		--itr2;
		l1 = *(itr2);
		--itr2;
		l2 = *(itr2);

		int cnt = (i - l1) * (u2 - u1) + (u1 - i) * (l1 - l2);
		sum += p * cnt;
		shown.insert(i);
	}
	cout << sum << endl;
	return 0;
}