Increasing Subsequence

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