#include<bits/stdc++.h>
using namespace std;
const int N=1e6;
int i,j,k,m,n,len;
int d[N],a[N];
bool cmp(int x,int y){return x>y;}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	d[1]=a[1];
	len=1;
	for(int i=2;i<=n;i++)
	{
		if(a[i]<=d[len]) d[++len]=a[i];
		else
		{
			int p=upper_bound(d+1,d+len+1,a[i],cmp)-d;
			d[p]=a[i];
		}
	}
	printf("%d\n",len);
}
### Prompt

Construct a cpp code solution to the problem outlined:

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;
const int N=1e6;
int i,j,k,m,n,len;
int d[N],a[N];
bool cmp(int x,int y){return x>y;}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	d[1]=a[1];
	len=1;
	for(int i=2;i<=n;i++)
	{
		if(a[i]<=d[len]) d[++len]=a[i];
		else
		{
			int p=upper_bound(d+1,d+len+1,a[i],cmp)-d;
			d[p]=a[i];
		}
	}
	printf("%d\n",len);
}
```