A. Local Extrematime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a. Some element of this array ai is a local minimum iff it is strictly less than both of its neighbours (that is, ai < ai - 1 and ai < ai + 1). Also the element can be called local maximum iff it is strictly greater than its neighbours (that is, ai > ai - 1 and ai > ai + 1). Since a1 and an 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.InputThe first line contains one integer n (1 ≤ n ≤ 1000) — the number of elements in array a.The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the elements of array a.OutputPrint the number of local extrema in the given array.ExamplesInput31 2 3Output0Input41 5 2 5Output2
Input31 2 3
Output0
['brute force', 'implementation', '*800']