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 <algorithm>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <queue>
#include <list>
#include <cmath>
#include <stack>
#include <iomanip>

using namespace std;
typedef long long ll;
using Pll = pair<ll,ll>;

const ll INF = 1LL<<60;
const ll MOD = 1000000007;

//cout << fixed << setprecision(10);

int main() {
    ll n;
    cin >> n;
    vector<ll> p(n);
    for(int i=0;i<n;i++) cin >> p[i];
    int ans=0;
    for(int i=0;i<n-2;i++){
        if(max(p[i],max(p[i+1],p[i+2]))!=p[i+1] && min(p[i],min(p[i+1],p[i+2]))!=p[i+1]){
            ans++;
        }
    }
    cout << ans << endl;

    return 0;
}