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

int main(){
	int N;
	cin >> N;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	int ans=1;
	multiset<int> m;
	m.insert(A[0]);
	
	for(int i=1;i<N;i++){
		
		auto it=m.lower_bound(A[i]);
		if(it==m.begin()){
			ans++;
			m.insert(A[i]);
		}
		else{
			it--;
			m.erase(it);
			m.insert(A[i]);
		}
	}
	cout << ans << endl;
	return 0;
}
### 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;
	cin >> N;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	int ans=1;
	multiset<int> m;
	m.insert(A[0]);
	
	for(int i=1;i<N;i++){
		
		auto it=m.lower_bound(A[i]);
		if(it==m.begin()){
			ans++;
			m.insert(A[i]);
		}
		else{
			it--;
			m.erase(it);
			m.insert(A[i]);
		}
	}
	cout << ans << endl;
	return 0;
}
```