# Longest Bitonic Subsequence

A sequence is called bitonic if it’s strictly increasing and then strictly decreasing. A sequence that is only strictly increasing is bitonic. Also, a sequence that is only strictly decreasing is bitonic.

Given a list of integers `nums`

, return the length of the longest bitonic subsequence.

**Constraints**

`n ≤ 1,000`

where`n`

is the length of`nums`

.

https://binarysearch.com/problems/Longest-Bitonic-Subsequence

## Examples

### Example 1

**Input**

- nums =
`[1, 3, 2, 5, 9]`

**Output**

- answer =
`4`

**Explanation**

`[1, 3, 5, 9]`

### Example 2

**Input**

- nums =
`[10, 2, 5, 7, 3, 1]`

**Output**

- answer =
`5`

**Explanation**

The longest bitonic subsequence is `[2, 5, 7, 3, 1]`

### Example 3

**Input**

- nums =
`[1, 0, 3, 2, 9, 4, 5, 2]`

**Output**

- answer =
`5`

**Explanation**

The longest bitonic subsequence is `[1, 3, 9, 5, 2]`

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