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

inputFormat

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

outputFormat

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

样例

9
9 6 3 2 5 8 7 4 1

5