#include <iostream>
#include <algorithm>
using namespace std;

long long N, S, A[1 << 18], B[1 << 18];

int main() {
	cin >> N;
	for (int i = 1; i <= N; i++) { cin >> A[i]; A[i] *= -1; }
	for (int i = 1; i <= N; i++) {
		int pos1 = lower_bound(B, B + S, A[i] + 1) - B;
		if (pos1 == S) { S++; }
		B[pos1] = A[i];
	}
	cout << S << 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 <algorithm>
using namespace std;

long long N, S, A[1 << 18], B[1 << 18];

int main() {
	cin >> N;
	for (int i = 1; i <= N; i++) { cin >> A[i]; A[i] *= -1; }
	for (int i = 1; i <= N; i++) {
		int pos1 = lower_bound(B, B + S, A[i] + 1) - B;
		if (pos1 == S) { S++; }
		B[pos1] = A[i];
	}
	cout << S << endl;
	return 0;
}
```