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>
#include <algorithm>
#include <math.h>
using namespace std;

template <class T> using V = vector<T>;
template <class S, class T> using P = pair<S, T>;
template <class... T> using TP = tuple<T...>;

using ll = long long;
using db = double;
using ldb = long db;
using str = string;
using vll = V<ll>;
using vvll = V<V<ll>>;
using pll = P<ll,ll>;
using tpll = TP<ll,ll,ll>;
using vpll =V<pll>;
using vst = V<str>;
using vch = V<char>;

#define FOR(i,a,b) for(ll i=(a);i<(ll)(b);i++)
#define rFOR(i,a,b) for(ll i=(b);i>(ll)(a);i--)
#define oFOR(i,a,b) for(ll i=(a);i<(ll)(b);i+=2)
#define bgn begin()
#define en end()
#define SORT(a) sort((a).bgn,(a).en)
#define REV(a) reverse((a).bgn,(a).en)
#define fi first
#define se second
#define sz size()
#define gcd(a,b) __gcd(a,b)
#define lcm(a,b) __lcm(a,b)
#define co(a) cout<<a<<endl
#define ci(a) cin>>a
#define pb(a) push_back(a)
#define pob pop_back()
#define mp make_pair
#define mt make_tuple
#define pbmp(a,b) push_back(mp(a,b))
#define subs(a,b) substr(a,b)
#define cfs(a) cout<<fixed<<setprecision(a)
#define INF 1e16
#define mod 1e9+7


int main() {
  ll n;
  cin>>n;
  vll v(n);
  FOR(i,0,n){
    cin>>v[i];
  }
  ll count=0;
  FOR(i,1,n-1){
    if(v[i]>v[i-1]&&v[i]<v[i+1]){
      count++;
    }
    if(v[i]<v[i-1]&&v[i]>v[i+1]){
      count++;
    }
  }
  co(count);
}