#include <bits//stdc++.h>
using namespace std;
int dp[100005], a[100005], n;
int LIS() {
  int len = 1;dp[0] = a[0];
  for (int i = 1; i < n; ++i) {
    if (a[i] >= dp[len - 1]) dp[len++] = a[i];
    else *upper_bound(dp, dp + len, a[i]) = a[i];
  }return len;
}
int main() {
  cin >> n;
  for (int i = n - 1; i >= 0; i--) cin >> a[i];
  cout << LIS() << endl;
}
### Prompt

Please create a solution in cpp 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;
int dp[100005], a[100005], n;
int LIS() {
  int len = 1;dp[0] = a[0];
  for (int i = 1; i < n; ++i) {
    if (a[i] >= dp[len - 1]) dp[len++] = a[i];
    else *upper_bound(dp, dp + len, a[i]) = a[i];
  }return len;
}
int main() {
  cin >> n;
  for (int i = n - 1; i >= 0; i--) cin >> a[i];
  cout << LIS() << endl;
}
```