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: Wrong Answer)

#include <bits//stdc++.h>
using namespace std;
int main(void){
    int a,b,c,ans,i,j;
    vector<int> v;
    cin>>a;
    for(i=0;i<a;i++){
        
        cin>>b;
        if(i==0)
        v.push_back(b);
        else if(v[v.size()-1]<b)
        v[v.size()-1]=b;
        else if(b<=v[0]){
            v.push_back(b);
            sort(v.begin(),v.end());
        }
        else{
            c=v.size()/2;
            int d=v.size();
            int e=0;
            while(1){
                if(v[c-1]<b<=v[c]){
                    v[c-1]=b;
                    break;
                }
                else if(v[c]<b){
                    e=c;
                    c=(d+e)/2;
                }
                else{
                    d=c;
                    c=(d+e)/2;
                }
            }
        }
        
    }
    
    cout<<v.size()<<endl;
}