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: Runtime Error)

#include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <map>
#include <iomanip>
#include <stdlib.h>
#include <queue>

using namespace std;

const int nmax = 1e9 + 7;
typedef long long ll;

int main(){

  int N; cin >> N;

  vector <int> P(N);
  for (int i = 0; i < N; i++) cin >> P[i];
  
  ll DP_first[N][N], DP_second[N][N];

  for (int i = 0; i < N; i++){
    DP_first[i][i] = P[i];
    DP_second[i][i] = 0;
  }

  ll ans = 0;
  for (int i = 0; i < N - 1; i++){
    for (int j = i + 1; j < N; j++){
      if (P[j] > DP_first[i][j - 1]){
        DP_second[i][j] = DP_first[i][j - 1];
        DP_first[i][j] = P[j];
      }else if(P[j] > DP_second[i][j - 1]){
        DP_first[i][j] = DP_first[i][j - 1];
        DP_second[i][j] = P[j];
      }else{
        DP_first[i][j] = DP_first[i][j - 1];
        DP_second[i][j] = DP_second[i][j - 1];
      }
      ans += DP_second[i][j];
    }
  }
  cout << ans << endl;
  

  return 0;
}