Given an array of integers, find the longest increasing subsequence.
A subsequence is just a collection of numbers from the array - however, they must be in order.

For example:
Array: $1,2,5,4,3,6$
The longest increasing subsequence here is $1,2,5,6$ (or $1,2,4,6$, or $1,2,3,6$).
The numbers must be strictly increasing - no two numbers can be equal.

Input Specification

$N\le 5000$, the number of integers.
$N$ lines, each with a value in the array.

Output Specification

The length of the longest increasing subsequence of the array.