#include<bits/stdc++.h>
#define int long long
using namespace std;
const int INF=1000000000000000;
int A[100100];
signed main(){
  int N;
  cin>>N;
  for(int i=0;i<N;i++)A[i]=INF;
  int ans=0;
  for(int i=0;i<N;i++){
    int a;
    cin>>a;
    int it=upper_bound(A,A+N,-a)-A;
    if(A[it]==INF)ans++;
    A[it]=-a;
  }
  cout<<ans<<endl;
}
### Prompt

Develop a solution in CPP to the problem described below:

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>
#define int long long
using namespace std;
const int INF=1000000000000000;
int A[100100];
signed main(){
  int N;
  cin>>N;
  for(int i=0;i<N;i++)A[i]=INF;
  int ans=0;
  for(int i=0;i<N;i++){
    int a;
    cin>>a;
    int it=upper_bound(A,A+N,-a)-A;
    if(A[it]==INF)ans++;
    A[it]=-a;
  }
  cout<<ans<<endl;
}
```