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: Accepted)

#include <bits/stdc++.h>
/*
#include<algorithm>
#include<array>
#include<cassert>
#include<cmath>
#include<cstdlib>
#include<functional>
#include<iomanip>
#include<iostream>
#include<map>
#include<numeric>
#include<queue>
#include<set>
#include<stack>
#include<string>
#include<typeinfo>
#include<utility>
#include<vector>
*/
#define int long long int
#define double long double
using namespace std;
#define MOD 1000000007
#define INF 1000000000000000007
const int MAX_N = 1 << 17;
#define rep(i, n) for (int(i) = 0, i##_len = (n); (i) < i##_len; (i)++)
#define reps(i, x) for (int(i) = 1; (i) <= (int)(x); (i)++)
#define rrep(i, x) for (int(i) = ((int)(x)-1); (i) >= 0; (i)--)
#define rreps(i, x) for (int(i) = ((int)(x)); (i) > 0; (i)--)
#define FOR(i, a, b) for (int(i) = (a); (i) < (b); (i)++)
#define pb push_back
#define mp make_pair
#define bit(n) ((int)(1) << (n))
#define all(x) (x).begin(), (x).end()
#define debug(x) std::cout << #x << ": " << (x) << std::endl
#define nint int
using namespace std;

int dy[] = {0, 0, 1, -1, 0};
int dx[] = {1, -1, 0, 0, 0};
typedef pair<int, int> pii;
typedef pair<double, double> dop;
template <class T>
bool chmax(T& a, const T& b)
{
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T& a, const T& b)
{
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
struct aaa {
    aaa()
    {
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout << fixed << setprecision(20);
    };
} aaaaaaa;


signed main()
{
    int n;
    cin >> n;
    std::vector<int> p(n);
    std::vector<int> place(n + 1);
    std::set<int> check;
    for(int i = 0; i < n; i++){
        cin >> p[i];
        place[p[i]] = i;
        if(p[i] == n){
            check.insert(i);
        }
    }
    int out = 0;
    for(int i = n - 1; i >= 1; i--){
        check.insert(place[i]);
        auto nowit = check.find(place[i]);
        int ll,l,r,rr;
        int flagl = 0;
        int flagr = 0;
        if(nowit == check.begin()){
            l = -1;
            ll = -1;
        } else if(std::next(nowit,-1) == check.begin()){
            l = *std::next(nowit,-1);
            ll = -1;
        } else {
            l = *std::next(nowit,-1);
            ll = *std::next(nowit, -2);
        }
        if(nowit == std::next(check.end(),-1)){
            r = n;
            rr = n;
        } else if(std::next(nowit,1) == std::next(check.end(),-1)){
            r = *std::next(nowit,1);
            rr = n;
        } else {
            r = *std::next(nowit,1);
            rr = *std::next(nowit, 2);
        }
        
        out += i * (r - place[i]) * (l - ll) + i * (place[i] - l) * (rr - r);
    }
    cout << out << endl;
    return 0;
}