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)

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define reps(i, n) for (int i = 1; i <= (n); ++i)
#define repd(i, n) for (int i = (n - 1); i >= 0; --i)
#define repds(i, n) for (int i = (n); i > 0; --i)
#define loop(i, x, n) for (int i = (x); i < (n); ++i)
#define loops(i, x, n) for (int i = (x); i <= (n); ++i)
#define loopd(i, x, n) for (int i = (x); i > (n); --i)
#define loopds(i, x, n) for (int i = (x); i >= (n); --i)
#define itrep(i, a) for (auto i = begin(a); i != end(a); ++i)
#define itrepd(i, a) for (auto i = rbegin(a); i != rend(a); ++i)
#define all(x) x.begin(), x.end()
using namespace std;
using ll = long long;
using ld = long double;
template <class T>
using priority_queuel = priority_queue<T, vector<T>, greater<T>>;
constexpr ll inf = static_cast<ll>(1e18);
constexpr int iinf = static_cast<int>(1e9);
constexpr double dinf = 1e10;
constexpr ld ldinf = 1e18;
constexpr double eps = 1e-9;
ll mod = static_cast<ll>(1e9 + 7);
template <class T>
constexpr int sz(const T &a) { return (int)a.size(); }
template <class T>
constexpr T pow2(const T a) { return a * a; }
template <class T, class... Args>
constexpr void mins(T &a, Args... args) { a = min<T>({a, args...}); }
template <class T, class... Args>
constexpr void maxs(T &a, Args... args) { a = max<T>({a, args...}); }
template <class A, int N, class T>
void fillArray(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); }

int n;
pair<ll, int> a[100005];
void solve() {
    cin >> n;
    rep(i, n) {
        cin >> a[i].first;
        a[i].second = i;
    }
    sort(a, a + n, greater<>());
    set<int> s;
    s.insert(-1);
    s.insert(n);
    ll ans = 0;
    rep(i, n) {
        auto p = s.insert(a[i].second).first;
        auto l = p;
        --l;
        auto r = p;
        ++r;
        if (l != s.begin()) {
            auto l2 = l;
            --l2;
            ans += a[i].first * (*l - *l2) * (*r - *p);
        }
        if (r != --s.end()) {
            auto r2 = r;
            ++r2;
            ans += a[i].first * (*p - *l) * (*r2 - *r);
        }
    }
    cout << ans << endl;
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    solve();
    return 0;
}