Given an array A$,$ find the length of the longest strictly increasing subsequence $($LIS$).$

A subsequence is a sequence that can be derived from an array by deleting some or no

elements such that the order of the remaining elements remain the same.

Example

$A$: $[10,20,2,5,3,8,8,25,6]$

Result: $4$

Explanation: Longest increasing subsequence: $[2,5,8,25]$