#include<bits/stdc++.h>
using namespace std;
const int maxn=1e6+5;
int a[maxn];
int d[maxn];
int main(){
	int i,j,k,m,n;
	cin>>n;
	for(i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	int top=0;
	for(i=n;i>=1;i--){
		if(a[i]>=d[top])d[++top]=a[i];
		else {
			int x=upper_bound(d+1,d+top+1,a[i])-d;
			d[x]=a[i];
		}
	}
	printf("%d\n",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<bits/stdc++.h>
using namespace std;
const int maxn=1e6+5;
int a[maxn];
int d[maxn];
int main(){
	int i,j,k,m,n;
	cin>>n;
	for(i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	int top=0;
	for(i=n;i>=1;i--){
		if(a[i]>=d[top])d[++top]=a[i];
		else {
			int x=upper_bound(d+1,d+top+1,a[i])-d;
			d[x]=a[i];
		}
	}
	printf("%d\n",top);
	return 0;
}
```