#include <bits/stdc++.h>
using namespace std;

int n,a[100010];

int main(){
    cin>>n;
    for(int i=0;i<n;i++)cin>>a[i];
    vector<int> b;
    b.push_back(a[0]);
    for(int i=1;i<n;i++){
        if(a[i]<=*b.begin()){
            b.insert(b.begin(),a[i]);
        }
        else{
            *(lower_bound(b.begin(),b.end(),a[i])-1)=a[i];
        }
    }
    cout<<b.size()<<endl;
}
### Prompt

Your challenge is to write 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[100010];

int main(){
    cin>>n;
    for(int i=0;i<n;i++)cin>>a[i];
    vector<int> b;
    b.push_back(a[0]);
    for(int i=1;i<n;i++){
        if(a[i]<=*b.begin()){
            b.insert(b.begin(),a[i]);
        }
        else{
            *(lower_bound(b.begin(),b.end(),a[i])-1)=a[i];
        }
    }
    cout<<b.size()<<endl;
}
```