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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main() {
    int N;
    scanf("%d", &N);
    int P[100000];
    for (int i=0; i < N; i++) scanf("%d", &P[i]);
    int r = 0;
    int fst;
    int sec;
    for (int i=0; i < N-1; i++) {
        fst = P[i];
        sec = 0;
        for (int j=i+1; j<N; j++) {
            int p = P[j];
            if (p > fst) {
                sec = fst;
                fst = p;
            } else if (p > sec) {
                sec = p;
            }
            r += sec;
        }
    }
    printf("%d\n", r);
    return 0;
}