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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

func scanLine() []int {
	var s []int
	scanner.Scan()
	for _, v := range strings.Split(scanner.Text(), " ") {
		i, _ := strconv.Atoi(v)
		s = append(s, i)
	}
	return s
}
func main() {
	var n int
	fmt.Scan(&n)
	p := scanLine()

	var result int
	for i := range p {
		if i == 0 || i == n-1 {
			continue
		}
		if p[i-1] < p[i] && p[i] < p[i+1] || p[i+1] < p[i] && p[i] < p[i-1] {
			result++
		}
	}
	fmt.Println(result)
}