Zigzag Sequence Checker

You are given a sequence of integers. Your task is to determine whether the given sequence is a Zigzag Sequence.

A sequence \(a_0, a_1, \ldots, a_{n-1}\) is called a Zigzag Sequence if for every index \(i\) (where \(1 \le i \le n-2\)) the following condition holds:

\[ (a_{i-1} a_{i+1}) \quad \text{or} \quad (a_{i-1} > a_i < a_{i+1}) \]

For sequences with fewer than two elements, or exactly two elements which are equal, the sequence is not considered a Zigzag Sequence.

Input Format: The first line contains a single integer \(n\) representing the number of elements in the sequence. If \(n > 0\), the second line contains \(n\) space-separated integers representing the sequence.

Output Format: Print True if the sequence is a Zigzag Sequence; otherwise print False.

inputFormat

The input is given from stdin and consists of:

• A single integer \(n\) (\(n \ge 0\)), the number of elements in the sequence.
• If \(n > 0\), a line with \(n\) space separated integers.

outputFormat

Output a single line to stdout containing either True or False depending on whether the sequence is a Zigzag Sequence.

## sample

0

False

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