#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
#define ALL(a) (a).begin(),(a).end()
int main(){
  int n;cin>>n;
  vector<int> v(n),a(n,1e9+1);
  rep(i,n) cin>>v[i];
  reverse(ALL(v));
  rep(i,n) a[upper_bound(ALL(a),v[i])-a.begin()]=v[i];
  cout<<lower_bound(ALL(a),1e9+1)-a.begin()<<endl;
}
### Prompt

Please formulate 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++)
#define ALL(a) (a).begin(),(a).end()
int main(){
  int n;cin>>n;
  vector<int> v(n),a(n,1e9+1);
  rep(i,n) cin>>v[i];
  reverse(ALL(v));
  rep(i,n) a[upper_bound(ALL(a),v[i])-a.begin()]=v[i];
  cout<<lower_bound(ALL(a),1e9+1)-a.begin()<<endl;
}
```