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)

/**
 *      purpose : 
 *      author  : kyomukyomupurin
 *      created : 
**/

// input/output
#include <iostream>
#include <fstream>
#include <sstream>
// container class
#include <array>
#include <deque>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
// math, algorithm
#include <algorithm>
#include <cmath>
#include <complex>
#include <numeric>
// etc
#include <bitset>
#include <cassert>
#include <cctype>
#include <cstring>
#include <chrono>
#include <iomanip>
#include <random>
#include <utility>
// using-directive
using namespace std;
// alias template
using int64 = int64_t;
using vi = vector<int>;
using vl = vector<int64_t>;
using pii = pair<int, int>;
using pll = pair<int64_t, int64_t>;
// text macro replacement
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define print(x) cout << (x) << '\n'
#define debug(x) cerr << #x << ": " << (x) << '\n'
// variadic template
template<typename T> inline void chmin(T &a, T b) {if (a > b) a = b; return;}
template<typename T> inline void chmax(T &a, T b) {if (a < b) a = b; return;}

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  int n; cin >> n;
  vector<int> p(n);
  rep(i, n) cin >> p[i];
  int cnt = 0;
  for (int i = 0; i < n - 2; ++i) {
    if ((p[i] < p[i + 1] && p[i + 1] < p[i + 2]) || (p[i] > p[i + 1] && p[i + 1] > p[i + 2])) {
      ++cnt;
    }
  }

  print(cnt);

  return 0;
}