#include<bits/stdc++.h>
using namespace std;
int n,a[200010],ans[200010],la;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n/2;i++) swap(a[i],a[n-i+1]);
	for(int i=1;i<=n;i++){
		if(ans[la]<=a[i]) ans[++la]=a[i];
		else{
			int p=upper_bound(ans+1,ans+la+1,a[i])-ans;
			ans[p]=a[i];
		}
	}
	cout<<la<<endl;
	return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

You are given a sequence with N integers: A = \\{ A_1, A_2, \cdots, A_N \\}. For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

* If A_i and A_j (i < j) are painted with the same color, A_i < A_j.



Find the minimum number of colors required to satisfy the condition.

Constraints

* 1 \leq N \leq 10^5
* 0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
A_1
:
A_N


Output

Print the minimum number of colors required to satisfy the condition.

Examples

Input

5
2
1
4
5
3


Output

2


Input

4
0
0
0
0


Output

4

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
int n,a[200010],ans[200010],la;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n/2;i++) swap(a[i],a[n-i+1]);
	for(int i=1;i<=n;i++){
		if(ans[la]<=a[i]) ans[++la]=a[i];
		else{
			int p=upper_bound(ans+1,ans+la+1,a[i])-ans;
			ans[p]=a[i];
		}
	}
	cout<<la<<endl;
	return 0;
}
```