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>
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define rrep(i,a,b) for(int i=(int)(a);i>=(int)(b);--i)
#define fore(i,a) for(auto &i:a)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define isin(i,a,b) ((a) <= (i) && (i) < (b))
#define uni(a) (a).erase(unique(all(a)),(a).end())
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)(a).size()
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
using ll  = long long;
using unit= unsigned;
using ull = unsigned long long;
using P   = pair<int,int>;
using vi  = vector<int>;
using vl  = vector<ll>;
using vvi = vector<vi>;
using vp  = vector<P>;
void _main(); int main(){ cin.tie(0); ios::sync_with_stdio(false); _main(); }
template<class T>void YES(T condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
template<class T>void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
template<class T>void POSS(T condition){ if(condition) cout << "POSSIBLE" << endl; else cout << "IMPOSSIBLE" << endl; }
template<class T>void Poss(T condition){ if(condition) cout << "Possible" << endl; else cout << "Impossible" << endl; }
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; }
template<class T>T gcd(T a, T b){ if (b==0){ return a; }else{ return gcd(b, a%b); }}
template<class T>T lcm(T a, T b){ return a / gcd(a, b) * b; }
constexpr double eps = 1e-10;
constexpr int inf = INT_MAX / 2;
constexpr ll infl = 1LL << 60;

void _main() {
  int N;
  cin >> N;
  vi p(N);
  rep(i, 0, N) cin >> p[i];

  int ans = 0;
  rep(i, 1, N-1) {
    if ((p[i-1] < p[i] && p[i] < p[i+1]) ||
        (p[i-1] > p[i] && p[i] > p[i+1])) ++ans;
  }
  cout << ans << endl;
}