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 <cstdlib>
#include <string>
#include <vector> // vectorを使うためにインクルードする

using namespace std;
int main(void){
    // Your code here!
    vector<int> arr; // <T>でT型のvector
    int count = 0,x,n = 0;
    cin >> n;
    
    while(cin >> x) {
		arr.push_back(x);
	}
    
    // while(cin>>l){
    //     arr[k] = l;
    //     k++;
    // }
    
    int a,b,c;
    
    for(int i = 0; i < n-2; i++){
        a = arr[i];
        b = arr[i+1];
        c = arr[i+2];
        
        if((a<b && b<c) || (c<b && b<a)){
            count ++;
        }
        
    }
    
        cout << count << endl; 
    
}