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 <iostream>
#include <stdio.h>
#include <bits/stdc++.h>
#include <queue>
#include <math.h>
#include <bitset>
#define INF 100000000000
#define N 10000000
#define ll long long
using namespace std;

int main(){
    ll n; cin>>n;
    vector<ll> que;
    ll a; cin>>a; que.push_back(a);
    ll count=1;
    for(ll i=0; i<n-1; i++){
        ll x; cin>>x;
        if(x>que.back()){
            que.back()=x;
            continue;
        }
        
        if(x<=que.front()){
            que.insert(que.begin(),x);
            count++;
            continue;
        }
        
        auto it=lower_bound(que.begin(),que.end(),x);
        ll index=it-que.begin();
        que[index-1]=x;
    }
    
    cout<<count<<endl;
}