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<iostream>
#include<vector>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<cmath>
#include<iomanip>
#include<cstring>
#define initdp(a,b) for(int i=0;i<=a;i++)for(int j=0;j<=b;j++)dp[i][j]=-1;
#define fi first
#define se second
#define pb push_back
#define pii pair<int,int>
#define ll long long
#define pll pair<ll,ll>
#define rep(i,n) for(int i=0;i<n;i++)
#define repd(i,n) for(int i=n-1;i>=0;i--)
#define waste ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define inf 1e9+1
#define inf1 1e18+1
#define mod 1000000007
#define pie 3.14159265358979323846
#define N 1000005
#define mid(l,r) l+(r-l)/2
using namespace std;
int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
int ddx[8]={1,1,0,-1,-1,-1,0,1},ddy[8]={0,1,1,1,0,-1,-1,-1};
void mad(ll &a,ll b){a=(a+b)%mod;if(a<0)a+=mod;}
ll gcd(ll a,ll b){ if(a>b)swap(a,b);if(!a)return b;return gcd(b%a,a);}

void solve(){
	int n;
	cin>>n;
	int a[n];
	rep(i,n)cin>>a[i];
	int c=0;
	for(int i=1;i<n-1;i++){
		int b[3];
		b[0]=a[i-1];
		b[1]=a[i];
		b[2]=a[i+1];
		sort(b,b+3);
		if(b[1]==a[i])c++;
	}
	cout<<c;
}
int main()
{
	waste;
	int t;
	//cin>>t;
	t=1;
	while(t--){
		solve();
	}
}