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)

//我是菜鸡
#include<bits/stdc++.h>
#define _for(i,a,b) for(int i = (a);i<(b);++i)
#define _defor(i,a,b) for((i) = (a);(i)<(b);++i)
#define _rfor(i,a,b) for(int i = (a);i>(b);--i)
#define _sfor(p,st) for(auto p:st)
#define debug(q,x) cout<<q<<x<<endl
using namespace std;
typedef long long ll;
const int INF = 0x3f3f3f3f;
const int maxn = 1e5+5;
const int MOD = 1e9 + 7;
const double ext = 1e-6;
int a[maxn];
void deprint() {
	//ofstream cout("E:\\acm dream\\debug.txt");
	return;
}
int main() {
	//ifstream cin("E:\\acm dream\\in.txt");5
	//ofstream cout("E:\\acm dream\\out.txt");
	//srand((unsigned)time(nullptr));
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	int a[25], n,so[3];
	while (cin >> n) {
		set<int>p;
		memset(a, 0, sizeof(a));
		_for(i, 0, n)cin >> a[i];
		_for(i, 0, n - 2) {
			so[0] = a[i], so[1] = a[i + 1], so[2] = a[i + 2];
			if (a[i] == a[i + 2] && a[i] == a[i + 1])continue;
			sort(so, so + 3);
			p.insert(so[1]);
		}
		cout << p.size() << endl;
	}
	return 0;
}