#include<bits/stdc++.h>
#define ll long long int
#define fast ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define pb push_back 
using namespace std;

int main()
{ 
  fast;
  ll n,x;
  cin>>n;

vector<ll> v;

for(ll i=0;i<n;i++)
{
  cin>>x;
  auto it=upper_bound(v.begin(),v.end(),-x);

  if(it==v.end())
    v.pb(-x);
  else *it=-x;
}
cout<<v.size()<<endl;
  }
### Prompt

Generate 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>
#define ll long long int
#define fast ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define pb push_back 
using namespace std;

int main()
{ 
  fast;
  ll n,x;
  cin>>n;

vector<ll> v;

for(ll i=0;i<n;i++)
{
  cin>>x;
  auto it=upper_bound(v.begin(),v.end(),-x);

  if(it==v.end())
    v.pb(-x);
  else *it=-x;
}
cout<<v.size()<<endl;
  }
```