You are given an array containing $n$ integers. Your task is to determine the longest increasing subsequence in the array, i.e., the longest subsequence where every element is larger than the previous one.
A subsequence is a sequence that can be derived from the array by deleting some elements without changing the order of the remaining elements.
The first line contains an integer $n$ : the size of the array.
After this there are $n$ integers $x_1,x_2,\ldots,x_n$ : the contents of the array.
Print the length of the longest increasing subsequence.