#include<bits/stdc++.h>
using namespace std;
const int M=1e5+5;
multiset<int>st;
multiset<int>::iterator it;
int n,A[M];

int main(){
	scanf("%d",&n);
	for(int i=1; i<=n; i++){
		scanf("%d",&A[i]);
	}
	for(int i=n; i>=1; i--){
		it=st.upper_bound(A[i]);
		if(it!=st.end()) st.erase(it);
		st.insert(A[i]);
	}
	printf("%d\n",st.size());
	return 0;
}
### Prompt

In Cpp, your task is to solve 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 M=1e5+5;
multiset<int>st;
multiset<int>::iterator it;
int n,A[M];

int main(){
	scanf("%d",&n);
	for(int i=1; i<=n; i++){
		scanf("%d",&A[i]);
	}
	for(int i=n; i>=1; i--){
		it=st.upper_bound(A[i]);
		if(it!=st.end()) st.erase(it);
		st.insert(A[i]);
	}
	printf("%d\n",st.size());
	return 0;
}
```