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)

a = input()
p_list = input().split()
N = len(p_list)
p_list1 = [int(i) for i in p_list]

current_value = 0

for L in range(N - 1):
    first_value = max(p_list1[L], p_list1[L + 1])
    second_value = min(p_list1[L], p_list1[L + 1])
    current_value += second_value
    for R in range(L + 2, N):
        if first_value < p_list1[R]:
            second_value = first_value
            first_value = p_list1[R]
        elif first_value >= p_list1[R] and second_value <= p_list1[R]:
            second_value = p_list1[R]

        current_value += second_value

print(current_value)