#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()
#define ll long long
int main(){
  int N;
  cin>>N;
  vector<int> A(N),B(N);
  rep(i,N) cin>>A[i];
  rep(i,N) A[i]=-A[i];
  rep(i,N) B[i]=1000000010;
  rep(i,N) *upper_bound(all(B),A[i])=A[i];
  cout<<lower_bound(all(B),1000000010)-B.begin()<<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;
#define rep(i,n) for(int i=0;i<(n);i++)
#define all(a) (a).begin(),(a).end()
#define ll long long
int main(){
  int N;
  cin>>N;
  vector<int> A(N),B(N);
  rep(i,N) cin>>A[i];
  rep(i,N) A[i]=-A[i];
  rep(i,N) B[i]=1000000010;
  rep(i,N) *upper_bound(all(B),A[i])=A[i];
  cout<<lower_bound(all(B),1000000010)-B.begin()<<endl;
}
```