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 <iostream>
#include <cstdint>
#include <cmath>
#include <string>
#include <vector>
#include <map>
#include <algorithm>

int main(void)
{
    int64_t n;
    std::cin >> n;

    std::vector<int64_t> values(n);
    for (auto& p : values) {
        std::cin >> p;
    }

    int64_t count = 0;
    for (int64_t i = 1; i < n-1; ++i) {
        if (values.at(i-1) <= values.at(i) && values.at(i) <= values.at(i+1)) count++;
        if (values.at(i-1) >= values.at(i) && values.at(i) >= values.at(i+1)) count++;
    }

    std::cout << count << std::endl;

    return 0;
}