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.

Input

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.

Output

Print the length of the longest increasing subsequence.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^9$

Example

Input:

8
7 3 5 3 6 2 9 8

Output:

4