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

const int INF = 1e9 + 1;

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

### Prompt

Your task is to create 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;

const int INF = 1e9 + 1;

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

```