Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
#define ll long long
ll dp[5009];
  ll a[5000];
int main()
{
  ll n;ll ans=0;
  multiset<ll>s;cin>>n;
  for(int i=0;i<n;i++){
      ll x;cin>>x;
      if(s.size()==0){
          s.insert(x);
          ans++;
          }
          else
          {
              auto z=s.begin();
              if(*z>=x){
                  s.insert(x);ans++
;              }else{
              auto it=s.lower_bound(x);it--;
              s.erase(s.find(*it));
               s.insert(x);
}
    
}
  }cout<<ans;

}