#include<bits/stdc++.h>

using namespace std;

#define INF 1145141919

int main(void){
  int N,i,ans=0;
  cin >> N;
  int A[N],dp[N];
  for(i=N-1;i>=0;i--){
    cin >> A[i];
  }
  fill(dp,dp+N,INF);
  for(i=0;i<N;i++){
    *upper_bound(dp,dp+N,A[i])=A[i];
  }
  ans=lower_bound(dp,dp+N,INF)-dp;
  cout << ans << endl;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 INF 1145141919

int main(void){
  int N,i,ans=0;
  cin >> N;
  int A[N],dp[N];
  for(i=N-1;i>=0;i--){
    cin >> A[i];
  }
  fill(dp,dp+N,INF);
  for(i=0;i<N;i++){
    *upper_bound(dp,dp+N,A[i])=A[i];
  }
  ans=lower_bound(dp,dp+N,INF)-dp;
  cout << ans << endl;
}
```