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>
#define reg register

using namespace std;

typedef long long ll;
const int maxn = 100005;

inline ll read() {
    reg ll s = 0, t = 0; reg char ch = getchar();
    while (!isdigit(ch)) t |= ch == '-', ch = getchar();
    while (isdigit(ch)) s = (s << 1) + (s << 3) + (ch ^ 48), ch = getchar();
    return t ? -s : s;
}

int n, a[maxn];
int main() {
    n = read(); reg int ans = 0;
    for (reg int i = 1; i <= n; i++) a[i] = read();
    for (reg int i = 2; i < n; i++) {
        if (a[i - 1] < a[i] && a[i] < a[i + 1]) ans++;
        else if (a[i + 1] < a[i] && a[i] < a[i - 1]) ans++;
    }
    cout << ans << endl;
    return 0;
}