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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<algorithm>//sort,二分探索,など
#include<bitset>//固定長bit集合
#include<cmath>//pow,logなど
#include<complex>//複素数
#include<deque>//両端アクセスのキュー
#include<functional>//sortのgreater
#include<iomanip>//setprecision(浮動小数点の出力の誤差)
#include<iostream>//入出力
#include<iterator>//集合演算(積集合,和集合,差集合など)
#include<map>//map(辞書)
#include<numeric>//iota(整数列の生成),gcdとlcm(c++17)
#include<queue>//キュー
#include<set>//集合
#include<stack>//スタック
#include<string>//文字列
#include<unordered_map>//イテレータあるけど順序保持しないmap
#include<unordered_set>//イテレータあるけど順序保持しないset
#include<utility>//pair
#include<vector>//可変長配列

// vectorの重複削除
// std::sort(test.begin(), test.end());
// test.erase(std::unique(test.begin(), test.end()), test.end());

using namespace std;
using ll = long long;
using P = pair<int, int>; // vector<P> ba(n); みたいな感じですぐ使える ba[i] = P(a, b); make_pairをしなくてもいい
// typedef vector<int> v;
template <class T>ostream &operator<<(ostream &o,const vector<T>&v){o<<"{";for(int i=0;i<(int)v.size();i++)o<<(i>0?", ":"")<<v[i];o<<"}";return o;}
#define debug(v) {cerr<<"\033[1;36m[debug]\033[m "<<#v<<" : "<<v<<endl;}
#define rep(i, c) for(int i = 0; i < int(c); i++)
#define ALL(x) (x).begin(), (x).end() //sort(ALL(obj))みたいな
#define SIZE(x) ((ll)(x).size()) //sizeをsize_tからllに直しておく
#define MAX(x) *max_element(ALL(x)) //最大値
#define pb push_back //
// const int MOD = 1000000007;
// string alpha="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
// printf("%.20f\n", ans); あれ
// const double PI = 3.141592653589793238462643383;

int main() {
  int n; cin>>n;
  std::vector<int> v(n);
  rep(i,n) cin>>v[i];
  int cnt=0;
  for(int i=0; i<n-2; i++){
    if ((v[i] < v[i+1] && v[i+1] < v[i+2]) || (v[i] > v[i+1] && v[i+1] < v[i+2])) cnt+=1;
  }
  cout << cnt << endl;
}