//https://atcoder.jp/contests/abc134/tasks/abc134_f
#include<bits/stdc++.h>

using namespace std;

const int N = 1e5 + 3;
int n,a[N],res = 0;

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for (int i = 1;i <= n;++i)
	{
		int p;
		cin >> p;
		int vt = upper_bound(a + 1,a + res + 1,p,greater<int>()) - a;
		res = max(res,vt);
		a[vt] = p;
	}
	cout << res; 
}
### Prompt

Your challenge is to write 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
//https://atcoder.jp/contests/abc134/tasks/abc134_f
#include<bits/stdc++.h>

using namespace std;

const int N = 1e5 + 3;
int n,a[N],res = 0;

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for (int i = 1;i <= n;++i)
	{
		int p;
		cin >> p;
		int vt = upper_bound(a + 1,a + res + 1,p,greater<int>()) - a;
		res = max(res,vt);
		a[vt] = p;
	}
	cout << res; 
}
```