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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<stdio.h>
#include<string>
#include<cmath>
#include<math.h>
#include<vector>
#include<queue>
#include<algorithm>
#include<map>
#include<unordered_map>
#define rep(i,n) for(int i = 0; i < (n); i++)
#define rep2(i,n) for(int i = -1; i < (n); i++)
#define PI 3.141592653589793

using namespace std;
using ll = long long;

const ll MA = 1000005;
int cnt[2];
int c[2];
int main() {

	int n;
	cin >> n;
	vector<int> p(n);
	int ans = 0;
	rep(i, n)cin >> p[i];

	for (int i = 1; i < n - 1; i++) {
		vector	<int> x;
		x.push_back(p[i - 1]);
		x.push_back(p[i]);
		x.push_back(p[i + 1]);

		sort(x.begin(), x.end());

		if (x[1] == p[i]) ans++; 

	}

	cout << ans << endl;

	return 0;
}