#include<cstdio>
#include<cstdlib>
#define rnt register int
using namespace std;
int d[100001];
int n,x;
int main()
{
	scanf("%d",&n);
	for(rnt i=0;i<100001;i=-~i)
		d[i]=-1;
	for(rnt i=0;i<n;i=-~i)
	{
		scanf("%d",&x);
		for(rnt j=0;;j=-~j)
			if(x>d[j])
			{
				d[j]=x;
				break;
			}
	}
	for(rnt i=0;i<=n;i++)
		if(d[i]==-1)
		{
			printf("%d\n",i);
			return 0; 
		}
}
### Prompt

Your challenge is to write 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<cstdio>
#include<cstdlib>
#define rnt register int
using namespace std;
int d[100001];
int n,x;
int main()
{
	scanf("%d",&n);
	for(rnt i=0;i<100001;i=-~i)
		d[i]=-1;
	for(rnt i=0;i<n;i=-~i)
	{
		scanf("%d",&x);
		for(rnt j=0;;j=-~j)
			if(x>d[j])
			{
				d[j]=x;
				break;
			}
	}
	for(rnt i=0;i<=n;i++)
		if(d[i]==-1)
		{
			printf("%d\n",i);
			return 0; 
		}
}
```