#include <bits/stdc++.h>
#define ALL(A) (A).begin(),(A).end()
#define rep(i,n) for(int i=0;i<(n);i++)   

using namespace std;  

int main(void){
	int N;
	cin >> N;
	vector<int> a(N);
	rep(i,N)cin >> a[i];
	deque<int> d;
	rep(i,N){
		int p = lower_bound(ALL(d),a[i]) - d.begin();
		if(p==0)d.push_front(a[i]);
		else d[p-1] = a[i];
	}
	cout << d.size() << endl;
}
### Prompt

In cpp, your task is to solve 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>
#define ALL(A) (A).begin(),(A).end()
#define rep(i,n) for(int i=0;i<(n);i++)   

using namespace std;  

int main(void){
	int N;
	cin >> N;
	vector<int> a(N);
	rep(i,N)cin >> a[i];
	deque<int> d;
	rep(i,N){
		int p = lower_bound(ALL(d),a[i]) - d.begin();
		if(p==0)d.push_front(a[i]);
		else d[p-1] = a[i];
	}
	cout << d.size() << endl;
}
```