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 $\displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}$.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \ldots P_N$

Output

Print $\displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}$.

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.

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

见题面 Input 部分

见题面 Output 部分