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 <vector>
#include <iostream>
#include <algorithm>
#include <queue>
#include <string>
#include <bitset>
#include <list>
#include <iomanip>
using namespace std;
#define rep(i,a,n) for(ll i=a;i<n;i++)
#define rrep(i,a,n) for(ll i=n;i>=a;i--)
#define elif else if
#define all(s) s.begin(),s.end()
typedef long long ll;
typedef pair<string,ll> P;
const ll INF = 1e+17;
const ll MODcdf = 998244353;
const ll MODatc = 1000000007;
bool pairCompare(const P& firstElof,const P& secondElof){
    return firstElof.first<secondElof.first;
}
bool pairCompare2(P firstElof,P secondElof){
    return (firstElof.second)%1000>(secondElof.second)%1000;
}
bool less_mod1000(int lhs, int rhs) {
  if ((lhs - rhs) % 1000 != 0)
    return lhs % 1000 < rhs % 1000;
  else // 5で割った余りが等しいなら普通に大小比較する
    return lhs < rhs;
}
string A="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string a="abcdefghijklmnopqrstuvwxyz";
ll dp[107000];
ll jump(ll start,ll goal){
  if(dp[start]>=0)return dp[start];
  if(start==goal){
    return 1;
  }elif(start>goal){
    return 0;
  }
  return dp[start]=(jump(start+1,goal)+jump(start+2,goal))%MODatc;
}
int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    ll n;cin>>n;
    ll p[n];
    ll ans=0;
    rep(i,0,n)cin>>p[i];
    rep(i,1,n-1){
      if(p[i]>=p[i-1]||p[i]>=p[i+1]){
        if(p[i]<=p[i-1]||p[i]<=p[i+1])ans++;
      }
    }
    cout<<ans<<endl;
}