#include<bits/stdc++.h>
using namespace std;

const long INF = 1e9+2;

int main(){
    long N;
    long A[100010];
    long dp[100010];

    cin >> N;
    fill(dp, dp+N, INF);
    for(long i=0;i<N;i++) cin >> A[i];
    reverse(A, A+N);
    for(int i=0;i<N;i++){
        *upper_bound(dp, dp+N, A[i]) = A[i];
    }
    cout << lower_bound(dp, dp+N, INF) - dp;
    return 0;
}
### Prompt

In Cpp, your task is to solve 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 INF = 1e9+2;

int main(){
    long N;
    long A[100010];
    long dp[100010];

    cin >> N;
    fill(dp, dp+N, INF);
    for(long i=0;i<N;i++) cin >> A[i];
    reverse(A, A+N);
    for(int i=0;i<N;i++){
        *upper_bound(dp, dp+N, A[i]) = A[i];
    }
    cout << lower_bound(dp, dp+N, INF) - dp;
    return 0;
}
```