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>

#define debug(n) cerr << #n << ':' << n << endl;

using namespace std;

using  ll = long long;

template<class T,class U>
using umap = unordered_map<T,U>;

template<class T>
using uset = unordered_set<T>;

template<class T>
inline bool change_max(T&a, const T&b){
  if(b > a){
    a = b;
    return true;
  }
  return false;
}

template<class T>
inline bool change_min(T&a, const T&b){
  if(a > b){
    a = b;
    return true;
  }
  return false;
}


int main(){
  int n; cin >> n;
  vector<int> v(n), idx(n);
  
  for(int&e:v){
    cin >> e;
    e--;
  }
  for(int i = 0; i < n; ++i){
    idx[v[i]] = i;
  }

  set<int> st;

  ll ans = 0;
  for(int i = n-1; i >= 0; --i){
    st.insert(idx[i]);
    ll a = -1, b = -1, c = n, d = n;
    auto it = st.find(idx[i]);

    ll x = *it;
    if(it != st.begin()){
      it--;
      b = *it;
      if(it != st.begin()){
	it--;
	a = *it;
      }
    }
    it = st.find(idx[i]);
    it++;
    if(it != st.end()){
      c = *it;
      it++;
      if(it != st.end()){
	d = *it;
      }
    }
    
    cerr << a << ' ' << b << ' ' << idx[i] << ' ' << c << ' ' << d << endl;

    ans += ((b - a) * (c - idx[i]) + (idx[i] - b) * (d - c)) * (i + 1);
  }

  cout << ans << endl;
  return 0;
}