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;
///////////////////////////////////////////
const long long int INF = 1LL<<60;
const long long int Mod = 1000000007;
using ll = long long int; using ci = const int;
using vi = vector<int>;  using Vi = vector<long long int>;
using P = pair<int, int>;  using PLL = pair<ll, ll>;
using matrix = vector<vector<ll>>;
#define pb(x) push_back(x)
#define mp(x,y) make_pair(x,y)
#define all(x) (x).begin(),(x).end()
#define rep(i,N) for(ll i = 0; i < (ll)N; i++)
#define repi(i,a,b) for(ll i = ll(a); i < ll(b); ++i)
template<class T>bool chmax(T &former, const T &b) { if (former<b) { former=b; return true; } return false; }
template<class T>bool chmin(T &former, const T &b) { if (b<former) { former=b; return true; } return false; }
template<class T>T sqar(T x){ return x*x; }//sqrt(x)は平方根;
#define Sort(v) std::sort(v.begin(), v.end(), std::greater<decltype(v[0])>()) //降順でVをソート
#define p_queue(v) priority_queue<v, vector<v>, greater<v> >
template<class T> inline void princ(T x){cout<<x<<" ";}; 
template<class T> inline void print(T x){cout<<x<<"\n";};
template<class T> inline void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
template<class T> inline void YES(T condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
///////////////////////////////////////////////////////////////////////////////////

ll n;
Vi p;

int main(){
    cin.tie(0);ios::sync_with_stdio(false);
    std::cout<<std::fixed<<std::setprecision(30);
    cin>>n;
    p.resize(n);
    rep(i,n){
        cin>>p[i];
    }
    ll a,b,c;
    ll ans = 0;
    rep(i,n-2){
        Vi v(3,0);
        v[0] = p[i];
        v[1] = p[i+1];
        v[2] = p[i+2];
        sort(all(v));
        if(v[1]==p[i+1])ans++;
    }
    print(ans);
    return 0;
}