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)

//inlclude前用define 
#define _USE_MATH_DEFINES

//include
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<cmath>
#include<type_traits>
#include<numeric>
//#include<deque>
#include<iomanip>
#include<set>
#include<tuple>
#include<map>

using namespace std;

//typedef
typedef vector<int> VI;
typedef vector<string> VS;
typedef vector<char> VC;
typedef long long int ll;

//define
#define INF 1e9 
#define NUM 1000000007
#define all(x) begin(x), end(x)
#define rep(i,n) for(int i=0;i<(int)(n);i++)

int main() {
    int n,cnt=0;
    cin>>n;
    VI p(n);
    rep(i,n) cin>>p[i];
    for(int i=1;i<n-1;i++){
      if(p[i-1]<p[i] && p[i]<p[i+1]){
        cnt++;
      }else if(p[i+1]<p[i] && p[i]<p[i-1]){
        cnt++;
      }
    }
    cout<<cnt<<endl;
}