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 <bits/stdc++.h>
#define MAXN 100010
#define pii pair<int,int>
#define ff first
#define ss second
#define ll long long
#define in_range(x, y, n) (x >= 0 and x<n and y >=0 and y<n)
using namespace std;
const int mod = 1e9 + 7;

int main (){
    int n;
    cin >> n;
    vector<int> v(n);

    for (int i=0; i<n; i++){
        cin >> v[i];
    }
    int ans = 0;
    for (int i=1; i<n-1; i++){
        if (v[i] != max(v[i], max(v[i-1], v[i+1])) and v[i] != min(v[i], min(v[i-1], v[i+1]))) ans++;
    }
    cout << ans << endl;
    return 0;
}