#include<cstdio>
#include<cstring> 
#include<iostream>
#include<set>
using namespace std;
#define INF 1000000000
int a[100005];
int n,ans=0;
multiset<int>l;
multiset<int>::iterator q;
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d",&a[i]);
q=l.lower_bound(a[i]);
if(q==l.begin()){
l.insert(a[i]);
ans++;
}
else {
q--;
l.erase(q);
l.insert(a[i]);
}
}
printf("%d\n",ans);
}

### Prompt

Please formulate 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<cstdio>
#include<cstring> 
#include<iostream>
#include<set>
using namespace std;
#define INF 1000000000
int a[100005];
int n,ans=0;
multiset<int>l;
multiset<int>::iterator q;
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d",&a[i]);
q=l.lower_bound(a[i]);
if(q==l.begin()){
l.insert(a[i]);
ans++;
}
else {
q--;
l.erase(q);
l.insert(a[i]);
}
}
printf("%d\n",ans);
}

```