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>
using namespace std;
#define pb push_back
#define all(v) v.begin(),v.end()
#define mem(arr) memset(arr, 0, sizeof(arr))
#define ff first
#define ss second
#define int long long int
const int MOD = 1e9 + 7;
const int INF = 1e18;
const int N = 1e6 + 20;
vector<int> g[N];
vector<int> vis(N);
int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int tc = 1;
    while(tc--){
        int n;
        cin >> n;
        int a[n];
        for(int i = 0; i < n; i++){
            cin >> a[i];
        }
        int ans = 0;
        for(int i = 1; i < n - 1; i++){
            vector<int> v = {a[i - 1], a[i], a[i + 1]};
            sort(all(v));
            if(v[1] == a[i]){
                ans++;
            }
        }
        cout << ans << '\n';
    }
}