Local Extrema

描述： 给出一个长度为n的数组a，定义： - 局部最大值：a[i]>a[i-1]且a[i]>a[i+1] - 局部最小值：a[i]<a[i-1]且a[i]<a[i+1] 局部极值既包含最大值也包含最小值。 由于a[1]和a[n]没有左/右邻接元素，所以不是局部最值。 请你统计数组a中局部最值的个数。 输入： 第一行一个整数n(1<=n<=1000)； 接下来的一行，有n个空格隔开的整数ai(1<=ai<=1000)。 输出： 一个整数，局部极值的个数。 感谢@Nishikino_Maki 提供的翻译

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 $ a_{1} $ 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.

The first line contains one integer $ n $ ( $ 1<=n<=1000 $ ) — the number of elements in array $ a $ . The second line contains $ n $ integers $ a_{1} $ , $ a_{2} $ , ..., $ a_{n} $ ( $ 1<=a_{i}<=1000 $ ) — the elements of array $ a $ .

Print the number of local extrema in the given array.

3
1 2 3

0

4
1 5 2 5

2