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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)

	p := make([]int, n)
	for i := range p {
		fmt.Scan(&p[i])
	}

	ans := 0
	for i := 1; i < n-1; i++ {
		switch {
		case p[i-1] == p[i] && p[i] == p[i+1]:
			continue
		case p[i] > p[i-1] && p[i] > p[i+1]:
			continue
		case p[i] < p[i-1] && p[i] < p[i+1]:
			continue
		}
		ans++
	}
	fmt.Println(ans)
}