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"
)

var sc = func() *bufio.Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	return sc
}()

func getInt() (n int) {
	sc.Scan()
	n, _ = strconv.Atoi(sc.Text())
	return n
}

func main() {
	sum := 0
	n := getInt()
	pArray := make([]int, n)
	for i := 0; i < n; i++ {
		pArray[i] = getInt()
	}

	for i := 0; i < n-2; i++ {
		if (pArray[i] < pArray[i+1] && pArray[i+1] < pArray[i+2]) ||
			(pArray[i] > pArray[i+1] && pArray[i+1] > pArray[i+2]) {
			sum++
		}
	}

	fmt.Println(sum)
}