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<vector>
#include<algorithm>
#include<cmath>
#include<string>
#include<tuple>
#include<utility>
#include<stack>
#include<queue>
#include<deque>
#include<set>
#include<iomanip>
#include<map>
using namespace std;
using ll=long long int;
typedef pair<int, int> P;
const int INF = 1e9 + 7;
int dx[4] = { 1,0,0,-1 };
int dy[4] = { 0,1,-1,0 };

int main() {
	
	int n;
	cin >> n;
	vector<int> p(n);
	for (int i = 0; i < n; i++) cin >> p[i];

	int cnt = 0;

	for (int i = 0; i < n - 2; i++) {
		if ((p[i] < p[i + 1] && p[i + 1] < p[i + 2])
			|| (p[i] > p[i + 1] && p[i + 1] > p[i + 2])) {
			cnt++;
		}
	}

	cout << cnt << endl;


	return 0;
}