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 int long long
using namespace std;
#define rep(i, n) for(int i=0;i<(n);++i)
typedef pair<int, int> pii;
const int INF = 1l << 60;
#define u_b upper_bound
#define l_b lower_bound

int N;
int P[22];

signed main() {
    cin >> N;
    rep(i, N) {
        cin >> P[i];
    }
    int ans = 0;
    for (int i = 1; i <= N - 2; ++i) {
        if (max({P[i - 1], P[i], P[i + 1]}) == P[i])continue;
        if (min({P[i - 1], P[i], P[i + 1]}) == P[i])continue;
        ans++;
    }
    cout << ans << endl;
    return 0;
}