#include <bits/stdc++.h>
using namespace std;
long long n,x,ans=0;
vector<long long> a,pt;
int main(){
	long long i,pos;
	cin>>n;
	for(i=0;i<n;i++)
	{
		cin>>x;
		a.push_back(x);
	}
	for(i=0;i<n;i++)
	{
		pos=lower_bound(pt.begin(),pt.end(),a[i])-pt.begin();
		if(pos==0)
		{
			pt.insert(pt.begin(),a[i]);
		}
		else
		{
			pt[pos-1]=a[i];
		}
	}
	cout<<pt.size()<<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;
long long n,x,ans=0;
vector<long long> a,pt;
int main(){
	long long i,pos;
	cin>>n;
	for(i=0;i<n;i++)
	{
		cin>>x;
		a.push_back(x);
	}
	for(i=0;i<n;i++)
	{
		pos=lower_bound(pt.begin(),pt.end(),a[i])-pt.begin();
		if(pos==0)
		{
			pt.insert(pt.begin(),a[i]);
		}
		else
		{
			pt[pos-1]=a[i];
		}
	}
	cout<<pt.size()<<endl;
	return 0;
}
```