#include <bits/stdc++.h>
#define REP(i,n) for(int i=0;i<(int)n;i++)
#define ALL(x) (x).begin(),(x).end()
using namespace std;
using ll=long long;

int main(){
  int N; cin>>N;
  int A[N]; REP(i,N) cin>>A[i];
  vector<ll> v={-1};
  REP(i,N) {
    auto itr=lower_bound(ALL(v),A[i]);
    if(itr==v.begin()) v.insert(v.begin(),A[i]);
    else *--itr=A[i];
  }
  cout<<v.size()<<endl;
}
### Prompt

Please formulate 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>
#define REP(i,n) for(int i=0;i<(int)n;i++)
#define ALL(x) (x).begin(),(x).end()
using namespace std;
using ll=long long;

int main(){
  int N; cin>>N;
  int A[N]; REP(i,N) cin>>A[i];
  vector<ll> v={-1};
  REP(i,N) {
    auto itr=lower_bound(ALL(v),A[i]);
    if(itr==v.begin()) v.insert(v.begin(),A[i]);
    else *--itr=A[i];
  }
  cout<<v.size()<<endl;
}
```