#include <bits/stdc++.h>

using namespace std;
const long long INF=1e9+7;
long long n, a[100009];
long long dp[100009];

int main(){
  cin >> n;
  fill(dp, dp+n+1, INF);
  for(int i=0;i<n;i++)cin >> a[i];
  for(int i=n-1;i>=0;i--){
    *upper_bound(dp, dp+n, a[i])=a[i];
  }
  for(int i=0;i<=n;i++){
    if(dp[i]==INF){
      cout << i << endl;
      return 0;
    }
  }
}


### Prompt

Create a solution in CPP for 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;
const long long INF=1e9+7;
long long n, a[100009];
long long dp[100009];

int main(){
  cin >> n;
  fill(dp, dp+n+1, INF);
  for(int i=0;i<n;i++)cin >> a[i];
  for(int i=n-1;i>=0;i--){
    *upper_bound(dp, dp+n, a[i])=a[i];
  }
  for(int i=0;i<=n;i++){
    if(dp[i]==INF){
      cout << i << endl;
      return 0;
    }
  }
}


```