Counting Peaks

You are given a list of integers representing altitudes. A peak is defined as an element which is strictly greater than its immediate neighbors. In other words, an index i (1 ≤ i ≤ n-2) is a peak if \(a_i > a_{i-1}\) and \(a_i > a_{i+1}\). Your task is to determine the number of peaks in the given array.

Constraints:

• 3 ≤ n ≤ 10⁶
• Each altitude is an integer.

Example: For an input array [1, 3, 2, 4, 1], there are 2 peaks (at indices 1 and 3), so the output is 2.

inputFormat

The first line contains a single integer n, the number of elements in the array.

The second line contains n space-separated integers representing the altitudes.

Input is read from standard input (stdin).

outputFormat

Output a single integer representing the number of peaks in the array.

Output should be written to standard output (stdout).

## sample

5
1 3 2 4 1

2