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# Longest Increasing Subsequence

Problem Description

Find the longest increasing subsequence of a given array of integers, A.

In other words, find a subsequence of array in which the subsequence's elements are in strictly increasing order, and in which the subsequence is as long as possible.

In this case, return the length of the longest increasing subsequence.

Problem Constraints

1 <= length(A) <= 2500
0 <= A[i] <= 2500

Input Format

The first and the only argument is an integer array A.

Output Format

Return an integer representing the length of the longest increasing subsequence.

Example Input

Input 1:

` A = [1, 2, 1, 5]`

Input 2:

` A = [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]`

Example Output

Output 1:

` 3`

Output 2:

` 6`

Example Explanation

Explanation 1:

` The longest increasing subsequence: [1, 2, 5]`

Explanation 2:

` The possible longest increasing subsequences: [0, 2, 6, 9, 13, 15] or [0, 4, 6, 9, 11, 15] or [0, 4, 6, 9, 13, 15]`

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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