p02988 AtCoder Beginner Contest 132 - Ordinary Number
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.

Examples

Input

5
1 3 5 4 2


Output

2


Input

9
9 6 3 2 5 8 7 4 1


Output

5
```python
N = int(input())
p = list(map(int,input().split()))

s = 0
for i in range(1,N-1):
    s += p[i-1] < p[i] < p[i+1] or p[i-1] > p[i] > p[i+1]

print(s)
```