Local Minimum Water Catching

You are given an array of integers representing the heights of hills. A hill at position (i) (with (1 \le i \le n-2)) is considered a local minimum if it satisfies the condition (h_i < h_{i-1}) and (h_i < h_{i+1}). Such a point can potentially hold water. Your task is to determine whether there exists at least one local minimum in the given array. Print True if there is at least one local minimum, otherwise print False.

inputFormat

The input is given via standard input (stdin). The first line contains an integer (n) ((0 \le n \le 10^5)) representing the number of hill heights. The second line contains (n) space-separated integers representing the hill heights.

outputFormat

Output a single line to standard output (stdout) containing either True if there exists at least one local minimum that can hold water, or False otherwise.## sample

8
1 2 1 3 4 3 1 2

True