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)

#define REP(i, t, n)  for (int i = t; i < n; i++)
#define ALL(n)        (n).begin(),(n).end()
#include <limits.h>
#include <stdio.h>
#include <cmath>
#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <map>
#include <queue>
#include <deque>
#include <functional>
#include <algorithm>
#include <cstring>
#include <unordered_map>
#include <numeric>

using namespace std;

typedef bool               BOOL;
typedef short              WORD;
typedef unsigned short     U_WORD;
typedef long               DWORD;
typedef unsigned long      U_DWORD;
typedef long long          QWORD;
typedef unsigned long long U_QWORD;

#define INF (100000)
#define N_MAX (20)

DWORD N;
DWORD adwInputP[N_MAX];

void solve_main()
{
	DWORD dwAns = 0;

	cin >> N;
	REP(i, 0, N) {
		cin >> adwInputP[i];
	}

	REP(i, 1, (N - 1)) {
		priority_queue<DWORD> que;
		for (int j = i - 1; j <= i + 1; j++) {
			que.push(adwInputP[j]);
		}
		que.pop();
		if (que.top() == adwInputP[i]) {
			dwAns++;
		}
	}
	cout << dwAns << endl;
}

int main()
{
#ifdef FOR_IDE
	ifstream in("input.txt");
	cin.rdbuf(in.rdbuf());
#endif

	solve_main();
	return 0;
}