#include <bits/stdc++.h>
using namespace std;
int N, top, A[200001], dec_len[200001];
int main(){
	cin >> N;
	for(int i=N; i>=1; --i) cin >> A[i];
	for(int i=1; i<=N; ++i) {
		if(A[i]>=dec_len[top]){
			dec_len[++top]=A[i];
		}else {
			dec_len[upper_bound(dec_len+1,dec_len+top+1,A[i])-dec_len]=A[i];
		}
	}
	cout << top << endl;
	return 0;
}
### 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;
int N, top, A[200001], dec_len[200001];
int main(){
	cin >> N;
	for(int i=N; i>=1; --i) cin >> A[i];
	for(int i=1; i<=N; ++i) {
		if(A[i]>=dec_len[top]){
			dec_len[++top]=A[i];
		}else {
			dec_len[upper_bound(dec_len+1,dec_len+top+1,A[i])-dec_len]=A[i];
		}
	}
	cout << top << endl;
	return 0;
}
```