#include <bits/stdc++.h>
using namespace std;
int a[100020],n,x;
int f[100020];
int main(){
    cin>>n;
    for(int i=0;i<n;i++){
    	cin>>a[i];
	}
    reverse(a,a+n);
    memset(f,0x3f,sizeof f);
    for(int i=0;i<n;i++){
        int p=upper_bound(f,f+n,a[i])-f;
        f[p]=a[i];
    }
    int ans2=lower_bound(f,f+n,0x3f3f3f3f)-f;
    cout<<ans2<<endl; 
}
### Prompt

Please create a solution in CPP 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 a[100020],n,x;
int f[100020];
int main(){
    cin>>n;
    for(int i=0;i<n;i++){
    	cin>>a[i];
	}
    reverse(a,a+n);
    memset(f,0x3f,sizeof f);
    for(int i=0;i<n;i++){
        int p=upper_bound(f,f+n,a[i])-f;
        f[p]=a[i];
    }
    int ans2=lower_bound(f,f+n,0x3f3f3f3f)-f;
    cout<<ans2<<endl; 
}
```