#include <bits/stdc++.h>
#define Int int64_t

using namespace std;

int main() {
	int N;
	cin >> N;
	vector<int> a(N);
	for (int i = 0; i < N; ++i) { cin >> a[i]; }

	multiset<int> st;
	st.insert(-a[0]);
	for (int i = 1; i < N; ++i) {
		auto it = st.upper_bound(-a[i]);
		if (it != st.end()) {
			st.erase(it);
		}
		st.insert(-a[i]);
	}
	cout << st.size() << endl;

	return 0;
}

### Prompt

Please formulate 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 <bits/stdc++.h>
#define Int int64_t

using namespace std;

int main() {
	int N;
	cin >> N;
	vector<int> a(N);
	for (int i = 0; i < N; ++i) { cin >> a[i]; }

	multiset<int> st;
	st.insert(-a[0]);
	for (int i = 1; i < N; ++i) {
		auto it = st.upper_bound(-a[i]);
		if (it != st.end()) {
			st.erase(it);
		}
		st.insert(-a[i]);
	}
	cout << st.size() << endl;

	return 0;
}

```