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<bits/stdc++.h>
using namespace std;
int st[100005];
int main()
{
    int g,t,x,q,w,e,r,nt,re=0;
    multiset<int>k;
    scanf("%d",&t);
    for(g=0;g<t;g++){
        scanf("%d",&x);
        st[--x]=g;
    }
    k.insert(-1),k.insert(-1),
    k.insert(t),k.insert(t);
    for(g=t-1;g>=0;g--){
        k.insert(st[g]);
        auto z=k.find(st[g]);
        z++, e=*z;
        z++, r=*z;
        z--, z--;
        z--, w=*z;
        z--, q=*z;
        nt=(((r-e)*(st[g]-w))+((w-q)*(e-st[g])));
        re+=(nt*(g+1));
    }
    printf("%d\n",re);
    return 0;
}