#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
const int MX = 100005;
const int INF = 1e9+7;
int n, a[MX], b[MX];
int main(){
	scanf("%d", &n);
	fill(b,b+n+1,INF);
	rep(i,n) scanf("%d", a+n-1-i);
	rep(i,n) *upper_bound(b,b+n,a[i]) = a[i];
	rep(i,n+1) if(b[i]==INF) return 0*printf("%d\n",i);
}
### Prompt

Your task is to create 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;
#define rep(i,n) for(int i=0; i<(n); i++)
const int MX = 100005;
const int INF = 1e9+7;
int n, a[MX], b[MX];
int main(){
	scanf("%d", &n);
	fill(b,b+n+1,INF);
	rep(i,n) scanf("%d", a+n-1-i);
	rep(i,n) *upper_bound(b,b+n,a[i]) = a[i];
	rep(i,n+1) if(b[i]==INF) return 0*printf("%d\n",i);
}
```