#include<bits/stdc++.h>
using namespace std;
int n,ans,a[100005],d[100005];
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i]; 
	int ans=1;d[1]=a[n];
	for(int i=n-1;i>=1;i--){
		int k=upper_bound(d+1,d+1+ans,a[i])-d;
		if(k>ans) d[++ans]=a[i];
		if(d[k]>a[i]) d[k]=a[i];
	}
	cout<<ans<<endl;
}

### 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,ans,a[100005],d[100005];
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i]; 
	int ans=1;d[1]=a[n];
	for(int i=n-1;i>=1;i--){
		int k=upper_bound(d+1,d+1+ans,a[i])-d;
		if(k>ans) d[++ans]=a[i];
		if(d[k]>a[i]) d[k]=a[i];
	}
	cout<<ans<<endl;
}

```