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 <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <deque>
#include <fstream>
#include <functional>
#include <iostream>
#include <istream>
#include <iterator>
#include <sstream>
#include <list>
#include <map>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <iomanip>
#define BR "\n"
#define REP(i,n) for(int (i)=0;(i)<(n);++(i))
#define ALL(cont) begin(cont),end(cont)
#define AS_MOD(a,b) ((((a) % (b) ) + (b)) % (b))
#define FEACH(it,cont) for(auto (it) = begin(cont); it!=end(cont);++it)
#define FEACHR(it,cont) for(auto (it) = rbegin(cont); it!=rend(cont);++it)
#define pb push_back
#define pob pop_back
#define fi first
#define se second
#define getll() ([](){ll s;scanf("%lld", &s);return s;})()
#define getld() ([](){ld s;scanf("%Lf", &s);return s;})()
#define prl(P) printf("%lld", P)
#define prd(P) printf("%.10Lf", P)
#define pr(P) printf(P)
#define MAX(V, T) V=max(V,T)

#define DumpArray(cont,from,to) for(int __i=from;__i<to;++__i) {cout<<"(" <<__i<<": " << cont[__i]<<")";} cout<<endl;

using namespace std;
typedef long long ll;
typedef long double ld;
int N;
vector<int> P;
int main() {
    cin >> N;
    P.resize(N);
    REP(i,N){
        cin >> P[i];
    }
    int ans=0;
    for(int i=1;i<N-1;++i){
        set<int> C;
        C.insert(P[i-1]);
        C.insert(P[i]);
        C.insert(P[i+1]);
        if (P[i]!=*C.begin() && P[i]!=*C.rbegin()){
            ans++;
        }
    }
    cout << ans << endl;
    return 0;
}