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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for(int (i)=0; (i)<(n); (i)++)

using namespace std;
typedef long long ll;

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int main()
{
  int N;
  cin >> N;

  vector<int> p(N);
  for(int i=0; i<N; i++)
    cin >> p[i];

  int count;
  for(int i=0; i<N-2; i++)
    {
      if(p[i]<p[i+1] && p[i+1]<p[i+2])
	count++;
      if(p[i+2]<p[i+1] && p[i+1]<p[i])
	count++;
      
    }

  cout << count << endl;


  return 0;
}


//cout << setprecision(13);
//next_permutation();
//__gcd();
//reverse();
//set ,tuple ,pair;
//bitset
//vector.find
//vector.count