#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,ans;
int q[N],f[N];
int dp[N],a[N];
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	memset(q,0x3f,sizeof(q));
	for(int i=1;i<=n;i++)
	{
		f[i]=upper_bound(q+1,q+n,-a[i])-q;
		q[f[i]]=-a[i];
		ans=max(ans,f[i]);
	}
	cout<<ans<<endl;
 } 
### 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
#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,ans;
int q[N],f[N];
int dp[N],a[N];
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	memset(q,0x3f,sizeof(q));
	for(int i=1;i<=n;i++)
	{
		f[i]=upper_bound(q+1,q+n,-a[i])-q;
		q[f[i]]=-a[i];
		ans=max(ans,f[i]);
	}
	cout<<ans<<endl;
 } 
```