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++ (GCC 5.4.1) (judge verdict: Wrong Answer)

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

int main() {
  int A,B,m,la,lb,ra,rb;
  A=0;
  int N,K;
  cin >> N;
  vector<int>p(N);
  for(int i=0;i<N;i++){
    cin >> p.at(i);
  }
  for(int n=1;n<(N+1);n++){
    la=n;
    lb=n;
    ra=N-n+1;
    rb=N-n+1;
    for(int i=1;i<n;i++){
      if(p.at(n-i-1)>p.at(n-1)){
        if(la==n){
          la=i;
        }else{
          lb=i;
        }
      }
    }
    for(int j=1;j<(N-n+1);j++){
      if(p.at(n+j-1)>p.at(n-1)){
        if(ra==N-n+1){
          ra=j;
        }else{
          rb=j;
        }
      }
    }

      A=A+((lb-la))*ra*p.at(n-1);
    
      A=A+((rb-ra))*la*p.at(n-1);
    
  }

cout << A << endl;


}