#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i=0; i<n; i++)
typedef long long ll;

int main() {
  int n; cin>>n;
  int a[n];
  deque<int> v;
  rep(i,n) cin>>a[i];
  
  rep(i,n){
    int p=lower_bound(v.begin(),v.end(),a[i])-v.begin();
    if(p==0){
      v.push_front(a[i]);
    }
    else{
      v[p-1]=a[i];
    }
  }
  
  cout<<v.size()<<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;
#define rep(i, n) for(int i=0; i<n; i++)
typedef long long ll;

int main() {
  int n; cin>>n;
  int a[n];
  deque<int> v;
  rep(i,n) cin>>a[i];
  
  rep(i,n){
    int p=lower_bound(v.begin(),v.end(),a[i])-v.begin();
    if(p==0){
      v.push_front(a[i]);
    }
    else{
      v[p-1]=a[i];
    }
  }
  
  cout<<v.size()<<endl;
    
}
```