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>

using namespace std;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n;
	cin >> n;
	vector <int> v(n);
	for (auto &x : v){
		cin >> x;
	}
	int res = 0;
	int i = 0;
	while ( i < n - 1){
		int tmp = v[i] + v[i+1] + v[i+2];
		int maxx = max(v[i],max(v[i+1],v[i+2]));
		int minn = min(v[i],min(v[i+1],v[i+2]));	
		int ans = tmp - maxx - minn;
		res++;
		if (ans == v[i]){	
			i+=1;
		}
		if (ans == v[i+1]){
			i+=2;
		}		
		if (ans == v[i+2]){
			i+=3;
		}	
	}
	cout << res;
	return 0;
}