p02988 AtCoder Beginner Contest 132 - Ordinary Number_16994
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
#include <cstdio>
int main()
{
	int a[25];
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", a + i);
	}
	int cnt = 0;
	for (int i = 1; i < n - 1; i++) {
		if ((a[i] - a[i - 1]) * (a[i] - a[i + 1]) < 0)
			cnt++;
	}
	printf("%d\n", cnt);
	return 0;
}