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- You 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.
- 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, ..., an (1 ≤ ai ≤ 1000) — the elements of array a.
- Output
- Print the number of local extrema in the given array.
- Example
- Input
- 3
- 1 2 3
- Output
- 0
- Input
- 4
- 1 5 2 5
- Output
- 2
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