#include<iostream>
#include<vector>
#include<queue>
using namespace std;

int main() {
	int n; cin >> n;
	vector<int> a(n);
	for (auto&& x : a) cin >> x;
	deque<int> d;
	for (int i = 0; i < n; i++) {
		int p = lower_bound(d.begin(), d.end(), a[i]) - d.begin();
		if (p == 0) d.push_front(a[i]);
		else d[p - 1] = a[i];		
	}
	cout << d.size() << endl;

	return 0;
}
### Prompt

Your task is to create 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<iostream>
#include<vector>
#include<queue>
using namespace std;

int main() {
	int n; cin >> n;
	vector<int> a(n);
	for (auto&& x : a) cin >> x;
	deque<int> d;
	for (int i = 0; i < n; i++) {
		int p = lower_bound(d.begin(), d.end(), a[i]) - d.begin();
		if (p == 0) d.push_front(a[i]);
		else d[p - 1] = a[i];		
	}
	cout << d.size() << endl;

	return 0;
}
```