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

Example Output

4