## Goal

Find the length of the longest increasing subsequence in a list.

A subsequence is a sequence of numbers that can be derived from the original list by deleting some or all of the elements without changing the order of the remaining elements. An increasing subsequence is a subsequence in which the elements are in increasing order.

Example:

Input: [5, 2, 8, 6, 3, 6, 9, 7]

Output: 4

If you remove 5, 8 and 6 (the first one) you get the longest increasing subsequence ([2, 3, 6, 9] or [2, 3, 6, 7]), both of which have a length of 4.
Input

**Line 1:** An integer `N` for the size of the list

**Next **`N` lines: An integer `P` that is part of the list

Output

**Line 1:** An integer that represents the length of the longest increasing subsequence

Constraints

2 <= `N` <= 2568