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)

/*
 *
 *   Author     : Amit Kumar
 *   Date    	: June 8 2019
 * 
 */

#include <bits/stdc++.h>

//#define FAST_INPUT_OUTPUT
//#define MORE_THAN_ONE_TESTCASE // COMMENT IT

#define vi vector<int>
#define vl vector<long long>
#define mii map<int , int>
#define mll map<long long , long long>
#define msi map<string , i>
#define msl map<string , long long>
#define umii unordered_map<int,int>
#define umll unordered_map<long long ,long long>
#define umsi unordered_map<string , int>
#define umsl map<string , long long> 
#define si set<int>
#define sl set<long long>
#define pii pair<int , int >
#define psi pair<string,int>
#define psl pair<string , long > 
#define pll pair<long long , long long>
#define vpii vector<pii>
#define vpll vector<pll>
#define vpsi vector<psi>
#define vpsl vector<psl>
#define pqi priority_queue<int>
#define pql priority_queue<long long>
#define ub upper_bound
#define lb lower_bound
#define bint long long int
#define ff first
#define ss second
#define all(x) x.begin(),x.end()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define iv(v) for(auto &i:v){cin>>i;}
#define ov(v) for(auto i:v){cout<<i<<" ";}cout<<endl;
#define ovn(v) for(auto i:v){cout<<i<<endl;}
#define euv(v) for(auto i:v){cerr<<i<<" ";}cerr<<endl;
#define eovn(v) for(auto i:v){cerr<<i<<endl;}
#define os(s) for(auto itr:s){cout<<itr<<" ";}cout<<endl;
#define osn(s) for(auto itr:s){cout<<itr<<endl;}
#define eos(s) for(auto itr:s){cerr<<itr<<" ";}cerr<<endl;
#define eosn(s) for(auto itr:s){cerr<<itr<<endl;}
#define rep(x) for(auto i=0 ; i<(x); ++i)
#define _rep(a,b) for(auto i=(a); i<(b); ++i)
#define endl '\n'
using namespace std;




auto SOLUTION_FUNCTION( void ) ->void {

    // your solution goes here 

    int n;

    cin>>n;

    vi v(n);
    iv(v);
    int counter = 0;
    for(int i=1; i<n-1;++i){
        if(v[i]<v[i+1] and v[i]>v[i-1])
            ++counter;
        else if(v[i]>v[i+1] and v[i]<v[i-1])
            ++counter;
    }
    cout<<counter<<endl;


    return ;
}




int main(void){
#ifdef FAST_INPUT_OUTPUT
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    cout<<setprecision(10);
    cout<<fixed;
    cout<<boolalpha;
#endif
#ifdef MY_LOCAL_PROJECT
    freopen("input","r",stdin);
    freopen("output","w",stdout);
#endif
    int testcase = 1;


#ifdef MORE_THAN_ONE_TESTCASE
    cin>>testcase;
#endif
    
    while(testcase--){
        SOLUTION_FUNCTION();
    }

#ifdef MY_LOCAL_PROJECT
    cout<<"Time : "<<1.0*(double)clock()/CLOCKS_PER_SEC<<endl;
#endif
    return 0;
}