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 pair<int, int> P;
using Graph = vector<vector<int>>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define Rep(i, k, n) for (int i = k; i < (int)(n); i++)
#define RRep(i, k, n) for (int i = k; i > (int)(n); i--)
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
#define ALL(a)  (a).begin(),(a).end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const long long INF = 1LL << 60;
const int MOD = 1000000007;
const double PI = acos(-1); //3.14~
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

int main()
{
    int n; cin >> n;
    int p[20];
    rep(i, n) cin >> p[i];

    int cnt = 0;
    Rep(i, 1, n - 1)
    {
        int tmp1 = min(p[i - 1], p[i]);
        int tmp2 = min(p[i], p[i + 1]);
        if (tmp1 != tmp2 && p[i] == max(tmp1, tmp2))
        {
            //COUT(p[i]);
            cnt++;
        }
    }
    cout << cnt << endl;
}