Longest Increasing Subsequence

Given an integer array `nums`, return _the length of the longest **strictly increasing **__**subsequence**_.   **Example 1:** **Input:** nums = [10,9,2,5,3,7,101,18] **Output:** 4 **Explanation:** The longest increasing subsequence is [2,3,7,101], therefore the length is 4. ``` **Example 2:** **Input:** nums = [0,1,0,3,2,3] **Output:** 4 ``` **Example 3:** **Input:** nums = [7,7,7,7,7,7,7] **Output:** 1 ```   **Constraints:** - `1 <= nums.length <= 2500` - `-104 <= nums[i] <= 104`   Follow up: Can you come up with an algorithm that runs in `O(n log(n))` time complexity?