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: Time Limit Exceeded)

from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)
# input = sys.stdin.readline
from math import factorial
import heapq, bisect
import math
import itertools


import queue
from collections import deque




def main():
    num = int(input())
    data = list(map(int, input().split()))

    for i in range(num):
        data[i] = (data[i], i + 1)
    data.sort(key=lambda x: -x[0])

    ind_list = [0, 0, num + 1, num + 1]
    ans = 0
    for i in range(num):
        ori_num, ori_ind = data[i]
        bisect.insort_left(ind_list, ori_ind)
        add_ind = bisect.bisect_left(ind_list, ori_ind)
        l2, l1 = ind_list[add_ind - 2], ind_list[add_ind - 1]
        r2, r1 = ind_list[add_ind + 2], ind_list[add_ind + 1]
        ans += ((l1 - l2) * (r1 - ori_ind) + (ori_ind - l1) * (r2 - r1)) * ori_num

    print(ans)


if __name__ == '__main__':
    main()