#include <bits/stdc++.h>
using namespace std;
vector<int> v;
int a[100005];
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	v.push_back(-1);
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<v.size();j++)
			if (a[i]>v[j])
			{
				v[j]=a[i];
				break;
			}
			else if (a[i]<=v[v.size()-1])
			{
				v.push_back(a[i]);
				break;
			}
	}
	cout<<(int)v.size();
	return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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;
vector<int> v;
int a[100005];
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	v.push_back(-1);
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<v.size();j++)
			if (a[i]>v[j])
			{
				v[j]=a[i];
				break;
			}
			else if (a[i]<=v[v.size()-1])
			{
				v.push_back(a[i]);
				break;
			}
	}
	cout<<(int)v.size();
	return 0;
}
```