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 rep(i, n) for (int i = 0; i < (int)(n); i++)
typedef long long ll;


void solve() {
  int N;
  scanf("%d", &N);
  int arr[N];
  rep(i,N) {
    scanf("%d", &arr[i]);
  }
  int ans=0;
  for (int i = 1; i < N-1; i++) {
    if ((max(arr[i-1],arr[i])==arr[i] && min(arr[i],arr[i+1])==arr[i])
          || (max(arr[i+1],arr[i])==arr[i] && min(arr[i],arr[i-1])==arr[i])) {
            ans++;
    }
  }

  cout << ans << "\n";
}

int main() {
  solve();
  return 0;
}