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