Problem:
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.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

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.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
p = list(map(int, input().split()))

ans = set()
for i in range(1, n-1):
	a = []
	a.append(p[i-1])
	a.append(p[i])
	a.append(p[i+1])
	a.sort()
	if a[0] < a[1] and a[1] < a[2]:
	  ans.add(a[1])
	elif a[0] == a[1]:
	 	ans.add(a[2])
	elif a[1] == a[2]:
		ans.add(a[1])
	
print(len(ans))