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: Wrong Answer)

#include <bits/stdc++.h>
#define SEKAI_NO_OWARI return 0;
#define INIT cin.tie(0); ios::sync_with_stdio(false);
#define rep(i, n) for(int i=0; i<n; i++)

using namespace std;

void solve() {
	int n; cin >> n;
	vector<int> p(n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &p[i]);
	}

	int res = 0;
	for (int i = 1; i < n - 1; i++) {
		if ((p[i - 1] < p[i]) && (p[i] < p[i + 1])) {
			res++;
		}
		else if ((p[i - 1] > p[i]) && (p[i] > p[i + 1])) {
			res++;
		}
	}
	cout << res << endl;
}

int main(void) {
	INIT;
	solve();
	return 0;
}