**Time limit:**1.00 s**Memory limit:**512 MB

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`