#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[100005],d[100005];
bool cmp(ll x,ll y){
    return x>y;
}
int main(){
    int n;
    cin>>n;
    for(int i=1;i<=n;i++){
        d[i]=-1;
        cin>>a[i];
    }
    for(int i=1;i<=n;i++){
        *upper_bound(d+1,d+1+n,a[i],cmp)=a[i];
    }
    cout<<lower_bound(d+1,d+1+n,-1,cmp)-d-1<<endl;
}
### 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;
typedef long long ll;
ll a[100005],d[100005];
bool cmp(ll x,ll y){
    return x>y;
}
int main(){
    int n;
    cin>>n;
    for(int i=1;i<=n;i++){
        d[i]=-1;
        cin>>a[i];
    }
    for(int i=1;i<=n;i++){
        *upper_bound(d+1,d+1+n,a[i],cmp)=a[i];
    }
    cout<<lower_bound(d+1,d+1+n,-1,cmp)-d-1<<endl;
}
```