#include<cstdio>
#include<algorithm>
using namespace std;
int n,dl[100005],len,a[100005];
int main() {
	scanf("%d",&n);
	for(int i=1; i<=n; i++) scanf("%d",&a[i]);
	len=1;
	dl[1]=a[n];
	for(int i=n-1; i>=1; i--) {
		int k=upper_bound(dl+1,dl+1+len,a[i])-dl;
		if(k>len) dl[++len]=a[i];
		if(dl[k]>a[i]) dl[k]=a[i];
	}
	printf("%d",len);
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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<cstdio>
#include<algorithm>
using namespace std;
int n,dl[100005],len,a[100005];
int main() {
	scanf("%d",&n);
	for(int i=1; i<=n; i++) scanf("%d",&a[i]);
	len=1;
	dl[1]=a[n];
	for(int i=n-1; i>=1; i--) {
		int k=upper_bound(dl+1,dl+1+len,a[i])-dl;
		if(k>len) dl[++len]=a[i];
		if(dl[k]>a[i]) dl[k]=a[i];
	}
	printf("%d",len);
}

```