#include <cstdio>
#include <cstdlib>
#include <algorithm>
using namespace std;
int st[200001],d[200001],top,n;
int main()
{
	scanf("%d",&n);
	for(int i=n; i>=1; --i)
		scanf("%d",&d[i]);
	for(int i=1; i<=n; ++i) {
		if(d[i]>=st[top])
			st[++top]=d[i];
		else {
			int loc=upper_bound(st+1,st+top+1,d[i])-st;
			st[loc]=d[i];
		}
	}
	printf("%d",top);
	return 0;
}
### 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 <cstdio>
#include <cstdlib>
#include <algorithm>
using namespace std;
int st[200001],d[200001],top,n;
int main()
{
	scanf("%d",&n);
	for(int i=n; i>=1; --i)
		scanf("%d",&d[i]);
	for(int i=1; i<=n; ++i) {
		if(d[i]>=st[top])
			st[++top]=d[i];
		else {
			int loc=upper_bound(st+1,st+top+1,d[i])-st;
			st[loc]=d[i];
		}
	}
	printf("%d",top);
	return 0;
}
```