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>

using namespace std;

typedef long long         ll;
typedef vector<int> vi;

#define pb(v)           push_back(v)
#define all(v)          v.begin(),v.end()
#define sz(v)           (int)v.size()
#define lp(i, n)		for(int i=0;i<(int)(n);++i)
#define lpi(i, j, n)	for(int i=(j);i<(int)(n);++i)
#define lpd(i, j, n)	for(int i=(j);i>=(int)(n);--i)
#define p(x)			cout<<#x<<" = { "<<x<<" }\n"
#define mp				make_pair


const int OO = (int)2e9;
const ll oo = 5e18;
const int M = 1e5+50;


int main()
{
    int n,a[20],x=0;
    cin >> n;
    lp(i,n)cin >> a[i];
    for(int i = 1;i<n-1;i++)
    {
        int f=0;
        if(a[i]>a[i-1])f++;
        if(a[i+1]>a[i])f++;
        if(f!=1)x++;
    }
    cout << x;
}