A wiggle sequence is a sequence where the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with one element and a sequence with two non-equal elements are trivially wiggle sequences.

- For example, `[1, 7, 4, 9, 2, 5]` is a wiggle sequence because the differences `(6, -3, 5, -7, 3)` alternate between positive and negative.
- In contrast, `[1, 4, 7, 2, 5]` and `[1, 7, 4, 5, 5]` are not wiggle sequences. The first is not because its first two differences are positive, and the second is not because its last difference is zero.

A subsequence is obtained by deleting some elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.

Given an integer array `nums`, return the length of the longest wiggle subsequence of `nums`.

Example 1:

    Input: nums = [1,7,4,9,2,5]
    Output: 6
    Explanation: The entire sequence is a wiggle sequence with differences (6, -3, 5, -7, 3).

Example 2:

    Input: nums = [1,17,5,10,13,15,10,5,16,8]
    Output: 7
    Explanation: There are several subsequences that achieve this length.
    One is [1, 17, 10, 13, 10, 16, 8] with differences (16, -7, 3, -3, 6, -8).

Example 3:

    Input: nums = [1,2,3,4,5,6,7,8,9]
    Output: 2

Constraints:

- `1 <= nums.length <= 1000`
- `0 <= nums[i] <= 1000`

Follow up: Could you solve this in `O(n)` time?