# Strictly Alternating List

You are given a list of integers `nums`

. Return whether the list alternates from first strictly increasing to strictly decreasing and then strictly increasing etc. If a list is only strictly increasing, return true.

**Constraints**

`2 ≤ n ≤ 100,000`

where`n`

is the length of`nums`

https://binarysearch.com/problems/Strictly-Alternating-List

## Examples

### Example 1

**Input**

- nums =
`[1, 2, 5, 7, 4, 1, 6, 8, 3, 2]`

**Output**

- answer =
`True`

**Explanation**

This list strictly increases, strictly decreases, strictly increases, then strictly decreases.

### Example 2

**Input**

- nums =
`[1, 1, 2, 3, 2, 1]`

**Output**

- answer =
`False`

**Explanation**

This list increases and then decreases, but is not strictly increasing at first.

### Example 3

**Input**

- nums =
`[1, 3, 5, 7]`

**Output**

- answer =
`True`

**Explanation**

This list is strictly increasing.

### Example 4

**Input**

- nums =
`[5, 3, 1, 5, 7]`

**Output**

- answer =
`False`

**Explanation**

This list is not strictly increasing at first.

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