#include<bits/stdc++.h>
using namespace std;
int n,a[100009],dp[100009],ans;
int main() {
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	dp[0]=1000000009;
	for(int i=1;i<=n;i++) {
		if(dp[ans]>=a[i]) {
			dp[ans+1]=a[i];
			ans++;
		}
		int l=0,r=ans;
		while(l<r) {
			int m=(l+r)/2;
			if(dp[m]>=a[i]) l=m+1;
			else r=m;
		}
		if(l!=0) dp[l]=a[i];
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Your task is to create 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<bits/stdc++.h>
using namespace std;
int n,a[100009],dp[100009],ans;
int main() {
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	dp[0]=1000000009;
	for(int i=1;i<=n;i++) {
		if(dp[ans]>=a[i]) {
			dp[ans+1]=a[i];
			ans++;
		}
		int l=0,r=ans;
		while(l<r) {
			int m=(l+r)/2;
			if(dp[m]>=a[i]) l=m+1;
			else r=m;
		}
		if(l!=0) dp[l]=a[i];
	}
	cout<<ans<<endl;
	return 0;
}
```