#include<iostream>
#include<algorithm>

using namespace std;

int N;
int A[100000];
int dp[100000];
const int INF = 1145141919;

int main() {
	cin >> N;
	for (int i = 0; i < N; i++)cin >> A[i], dp[i] = INF;
	reverse(A, A + N);
	for (int i = 0; i < N; i++) {
		*upper_bound(dp, dp + N, A[i]) = A[i];
	}

	cout << (lower_bound(dp, dp + N, INF) - dp) << endl;
	return 0;
}
### Prompt

Please provide a CPP coded solution 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<iostream>
#include<algorithm>

using namespace std;

int N;
int A[100000];
int dp[100000];
const int INF = 1145141919;

int main() {
	cin >> N;
	for (int i = 0; i < N; i++)cin >> A[i], dp[i] = INF;
	reverse(A, A + N);
	for (int i = 0; i < N; i++) {
		*upper_bound(dp, dp + N, A[i]) = A[i];
	}

	cout << (lower_bound(dp, dp + N, INF) - dp) << endl;
	return 0;
}
```