Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,

Given `[10, 9, 2, 5, 3, 7, 101, 18]`

,

The longest increasing subsequence is `[2, 3, 7, 101]`

, therefore the length is `4`

. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(*n*^{2}) complexity.

**Follow up:** Could you improve it to O(*n* log *n*) time complexity?

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