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-----
3
2 3 1

-----Sample Output-----
5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.

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