#include <iostream>
#include <algorithm>
using namespace std;
int n;
int a[100005],b[100005];
int len;
int main()
{
	cin>>n;
	for (int i=1;i<=n;i++)
	   cin>>a[i];

	b[1]=-a[1],len=1;

	for (int i=2;i<=n;i++)
		if (-a[i]>=b[len]) b[++len]=-a[i];
		else b[upper_bound(b+1,b+len,-a[i])-b]=-a[i];

	cout<<len<<endl;
}
### Prompt

In cpp, your task is to solve 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 <iostream>
#include <algorithm>
using namespace std;
int n;
int a[100005],b[100005];
int len;
int main()
{
	cin>>n;
	for (int i=1;i<=n;i++)
	   cin>>a[i];

	b[1]=-a[1],len=1;

	for (int i=2;i<=n;i++)
		if (-a[i]>=b[len]) b[++len]=-a[i];
		else b[upper_bound(b+1,b+len,-a[i])-b]=-a[i];

	cout<<len<<endl;
}
```