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<algorithm>
#include<vector>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<tuple>
#include<set>


#define MOD 1000000007
#define rep(i,k,N) for(int i=k;i<N;i++)
#define MP make_pair
#define MT make_tuple //tie,make_tuple は別物
#define PB push_back

typedef long long ll;

using namespace std;

int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};

int main(){
    int N;
    cin>>N;
    vector<int> P(N);
    rep(i,0,N)cin>>P[i];
    rep(i,0,N)P[i]--; //0-index
    
    vector<int> place(N);
    rep(i,0,N)place[P[i]]=i;

    set<int> visited;
    vector<int> l(2,-1),r(2,N);

    ll cnt=0;
    ll ans=0;
    for(int i=N-1;i>=0;i--){
        cnt=0;
        l[0]=-1;l[1]=-1;r[0]=N;r[1]=N;
        visited.insert(place[i]);
        auto it=visited.find(place[i]);

        rep(j,0,2){
            if(it==visited.begin())break;
            it--;
            l[j]=*it;
        }
        it=visited.find(place[i]);

        rep(j,0,2){
            it++;
            if(it==visited.end())break;
            r[j]=*it;
        }

        cnt+=(ll)((l[0]-l[1])*(r[0]-place[i])*(i+1));
        cnt+=(ll)((r[1]-r[0])*(place[i]-l[0])*(i+1));
        ans+=cnt;
    }
    cout<<ans<<endl;

    return 0;
}