Contest Duration: - (local time) (100 minutes) Back to Home
B - Ordinary Number /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

{1,\ 2,\ ...,\ n} の順列 p = {p_1,\ p_2,\ ...,\ p_n} があります。

• p_{i - 1},\ p_i,\ p_{i + 1}3 つの数の中で、p_i2 番目に小さい。

### 制約

• 入力は全て整数である。
• 3 \leq n \leq 20
• p は {1,\ 2,\ ...,\ n} の順列である。

### 入力

n
p_1 p_2 ... p_n


### 入力例 1

5
1 3 5 4 2


### 出力例 1

2


p_1 = 1,\ p_2 = 3,\ p_3 = 5 の中で、p_2 = 32 番目に小さい数です。また、p_3 = 5,\ p_4 = 4,\ p_5 = 2 の中で、p_4 = 42 番目に小さい数です。条件を満たす要素はこの 2 つです。

### 入力例 2

9
9 6 3 2 5 8 7 4 1


### 出力例 2

5


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