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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

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

int main(){
 int N; int i=0; int m=0; int tem; int vt; int ch=0; int k;
 cin >> N; 
 vector<int> aa; vector<int> bb;
 while(i++ < N){
     cin >> tem;
     aa.push_back(tem);
 }

bool jj = true; int t=0;
 for(int j=0; j<N; j++){
     tem = 5;
     for(k=0; k<bb.size(); k++){
         if(bb.at(k) < aa.at(j)){
            if(tem > bb.at(k)){
                t=k;
                tem = bb.at(k);
                jj=false;
            }
         }
     }
     if(jj==true){
     bb.push_back(aa.at(j));
     }else{
     bb.at(t) = tem;
     }
     jj=true;
 }
 cout << bb.size() << endl;
 return 0;
}