#include<bits/stdc++.h>
using namespace std;

int main(){
  int n,a;
  multiset<int> s;
  cin>> n;
  for (int i=0; i<n; i++){
    cin>> a;
    s.insert(a);
    auto itr=s.lower_bound(a);
    if (itr!=begin(s)) s.erase(--itr); //値指定は一致した値全て消去する。単一要素の削除ならイテレータ指定が良い。
  }
  cout<< s.size() <<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>
using namespace std;

int main(){
  int n,a;
  multiset<int> s;
  cin>> n;
  for (int i=0; i<n; i++){
    cin>> a;
    s.insert(a);
    auto itr=s.lower_bound(a);
    if (itr!=begin(s)) s.erase(--itr); //値指定は一致した値全て消去する。単一要素の削除ならイテレータ指定が良い。
  }
  cout<< s.size() <<endl;
}
```