#include<bits/stdc++.h>
using namespace std;
int N;
 int A [ 101010 ];

int V [ 101010 ];
 int num [ 101010 ];

void solve(){
	 int i,j,k,l,r,x,y; string s;
	
	
	cin >> N;
	multiset < int > M;
	for (int i=1;i<=N;i++){
		cin >> x;
		auto it = M.lower_bound(x);
		 if(it!= M.begin())M.erase(--it);
		M.insert(x);
	}
	cout << M.size()<< endl;
	
}

int main()
{
	solve();
	return 0;
}
### Prompt

Please create a solution in CPP 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;
int N;
 int A [ 101010 ];

int V [ 101010 ];
 int num [ 101010 ];

void solve(){
	 int i,j,k,l,r,x,y; string s;
	
	
	cin >> N;
	multiset < int > M;
	for (int i=1;i<=N;i++){
		cin >> x;
		auto it = M.lower_bound(x);
		 if(it!= M.begin())M.erase(--it);
		M.insert(x);
	}
	cout << M.size()<< endl;
	
}

int main()
{
	solve();
	return 0;
}
```