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: Time Limit Exceeded)

#include "bits/stdc++.h"
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
using ll =long long;
using P =pair<int,int>;

int main(){
    ll n;
    cin >> n;
    vector <ll> a(n);
    rep(i,n){
        cin >> a[i];
    }

    vector <ll> ans;
    ans.push_back(a[0]);
    ans.push_back(1001001001001001);
    
    ll r,l,m;

    rep(i,n){
        if(i!=0){
            if(a[i]<=ans[0]){
                ans.push_back(a[i]);
                sort(ans.begin(),ans.end());
            }
            else{
                r=ans.size();
                l=0;
                while(r-l>1){
                    m=(r+l)/2;
                    if(ans[m]<a[i]){
                        l=m;
                    }
                    else{
                        r=m;
                    }
                }
                ans[l]=a[i];   
            }
        }
    }

    cout << ans.size()-1 << endl;
    

    return 0;
}