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 PyPy3 (2.4.0) (judge verdict: Accepted)

from sys import stdin

if __name__ == '__main__':
    n = int(stdin.readline().rstrip())
    p = list(map(int, stdin.readline().rstrip().split()))

    def get_nexts(p):
        d, e = [n for i in range(n)], [n for i in range(n)]
        stack1, stack2 = [], []
        for i in range(n):
            while stack2 and p[stack2[-1]] < p[i]:
                idx = stack2.pop()
                e[idx] = i

            to_append = []
            while stack1 and p[stack1[-1]] < p[i]:
                idx = stack1.pop()
                d[idx] = i
                to_append.append(idx)

            while to_append:
                stack2.append(to_append.pop())
            stack1.append(i)

        dist1, dist2 = [], []
        for i in range(n):
            dist1.append(d[i] - i)
            dist2.append(e[i] - d[i])
        return dist1, dist2

    dist1, dist2 = get_nexts(p)
    dist3, dist4 = get_nexts(p[::-1])
    dist3, dist4 = dist3[::-1], dist4[::-1]

    ans = 0
    for i in range(n):
        ans += (dist1[i] * dist4[i] + dist2[i] * dist3[i]) * p[i]
    print(ans)