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;
using ll  = long long;
using ii  = pair < int , int >;
using i3  = pair < int , ii >;
using vi  = vector < int >;
using vii = vector < ii >;
using vi3 = vector < i3 >;

const int N = 25;
const ll INF = 1e12;
const double eps = 1e-9 , PI = acos(-1);

int n , m;
int a[N];

void solve(){
    scanf("%d" , &n);
    for(int i = 0 ; i < n ; i ++){
        scanf("%d" , &a[i]);
    }
    int ans = 0;
    for(int i = 1 ; i < n-1 ; i ++){
        vi tmp({a[i-1] , a[i] , a[i+1]});
        sort(tmp.begin() , tmp.end());
        if(tmp[1] == a[i])ans ++;
    }
    printf("%d\n" , ans);

}

main(){
    int t = 1;
    //scanf("%d" , &t);

    while( t -- ){
            solve();
    }

    return 0;
}