Score : $200$ points

Problem Statement

We have a permutation $p$ = {$p_1,\ p_2,\ ...,\ p_n$} of {$1,\ 2,\ ...,\ n$}.

Print the number of elements $p_i$ ($1 < i < n$) that satisfy the following condition:

• $p_i$ is the second smallest number among the three numbers $p_{i - 1}$, $p_i$, and $p_{i + 1}$.

Constraints

• All values in input are integers.
• $3 \leq n \leq 20$
• $p$ is a permutation of {$1,\ 2,\ ...,\ n$}.

Input

Input is given from Standard Input in the following format:

$n$

$p_1$ $p_2$ $...$ $p_n$

Output

Print the number of elements $p_i$ ($1 < i < n$) that satisfy the condition.

5
1 3 5 4 2

2

$p_2 = 3$ is the second smallest number among $p_1 = 1$, $p_2 = 3$, and $p_3 = 5$. Also, $p_4 = 4$ is the second smallest number among $p_3 = 5$, $p_4 = 4$, and $p_5 = 2$. These two elements satisfy the condition.

9
9 6 3 2 5 8 7 4 1

5