#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++) 
using namespace std;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  rep(i,N) cin >> A[i];
  deque<int> d;

  rep(i,N){
    int p = lower_bound(d.begin(),d.end(),A[i]) - d.begin();
    if(p == 0){
      d.push_front(A[i]);
    } else d[p-1] = A[i];
  }
  int ans = d.size();
  cout << ans << endl;
}
### 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>
#define rep(i,n) for(int i=0;i<(n);i++) 
using namespace std;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  rep(i,N) cin >> A[i];
  deque<int> d;

  rep(i,N){
    int p = lower_bound(d.begin(),d.end(),A[i]) - d.begin();
    if(p == 0){
      d.push_front(A[i]);
    } else d[p-1] = A[i];
  }
  int ans = d.size();
  cout << ans << endl;
}
```