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

Examples

Input

3
2 3 1

Output

5

Input

5
1 2 3 4 5

Output

30

Input

8
8 2 7 3 4 5 6 1

Output

136

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