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 <iomanip>
#include <stdio.h>
#include <cstring>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <functional>
#include <math.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;

int main() {
  int N; cin >> N;
  vector<int> P(N+1), I(N+1);
  for (int i = 1; i <= N; i++) {
    cin >> P[i];
    I[P[i]] = i;
  }
  set<int> S, SR;
  S.insert(I[N]);
  SR.insert(-I[N]);
  int ll, l, r, rr, ans = 0;
  for (int x = N-1; x > 0; x--) {
    int i = I[x];
    auto li = SR.upper_bound(-i);
    if (li == SR.end()) {
      l = ll = 0;
    } else {
      l = -*li;
      auto lli = SR.upper_bound(-l);
      if (lli == SR.end()) {
        ll = 0;
      } else {
        ll = -*lli;
      }
    }
    auto ri = S.upper_bound(i);
    if (ri == S.end()) {
      r = rr = N+1;
    } else {
      r = *ri;
      auto rri = S.upper_bound(r);
      if (rri == S.end()) {
        rr = N+1;
      } else {
        rr = *rri;
      }
    }
    ans += x*(l-ll)*(r-i)+x*(rr-r)*(i-l);
    S.insert(i);
    SR.insert(-i);
  }
  cout << ans << endl;
}