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: Wrong Answer)

/*
*          Name : chaitanya
*
*     Institute : ANITS,Visakhapatnam
*
*/
#include<cstdio>
#include <iostream>
#include<sstream>
#include<fstream>
#include<iomanip>
#include<algorithm>
#include<cmath>
#include<complex>
#include <cstring>
#include<vector>
#include<list>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<bitset>
#include<numeric>
#include<limits>
#include<climits>
#include<cfloat>
#include<functional>
#include<iterator>
#include <random>
#define inf  1000000000
#define mod  1e9+1
#pragma GCC optimization ("O3")
using namespace std;
const long long int N = 6999999;
#define all(x) begin(x),end(x)
int main()
{
 
  // freopen("input.txt","r",stdin);
  // freopen("output.txt","w",stdout);
  //ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
 int n;
 cin >> n;
 vector <int> v(n);
 set<int> ans;
 for (int i = 0; i < n; ++i)
 {
  cin >> v[i];
 }
 
 for (int i = 1; i < n-1; ++i)
 {
  int a[3] = {v[i-1],v[i],v[i+1]};
  sort(a,a+3);
  ans.insert(a[1]);
 }
 cout << ans.size();
  return 0;
}