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