Local Extrema

1000ms

262144K

Description:

You are given an array a. Some element of this array a_i is a local minimum iff it is strictly less than both of its neighbours (that is, a_i < a_i - 1 and a_i < a_i + 1). Also the element can be called local maximum iff it is strictly greater than its neighbours (that is, a_i > a_i - 1 and a_i > a_i + 1). Since a₁ and a_n have only one neighbour each, they are neither local minima nor local maxima.

An element is called a local extremum iff it is either local maximum or local minimum. Your task is to calculate the number of local extrema in the given array.

Input:

The first line contains one integer n (1 ≤ n ≤ 1000) — the number of elements in array a.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 1000) — the elements of array a.

Output:

Print the number of local extrema in the given array.

Sample Input:

3
1 2 3

Sample Output:

Sample Input:

4
1 5 2 5

Sample Output:

Informação

Provedor Codeforces

Código CF888A