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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;


typedef struct {
    int first;
    int second;
} txlr;

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

    int P[N];
    for ( int i = 0; i < N; i ++ ) cin >> P[i];

    long total = 0;
    int first, second;
    for ( int L = 0; L < N-1; L ++ ) {
        first = 0;
        second = 0;
        first = P[L];
        for ( int R = L+1; R < N; R ++  ) {
            if ( first < P[R] ) {
                second = first;
                first = P[R];
            } else if ( second < P[R] ) {
                second = P[R];
            }
//            cout << "L " << L << " R " << R << " " << first << " " << second << endl;

            total += second;
        }
    }

    cout << total << endl;

    return 0;
}