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: Accepted)

#include <algorithm>
#include <iostream>
#include <limits.h>
#include <math.h>
#include <queue>
#include <set>
#include <stdlib.h>
#include <string>
#include <vector>
#include <cstdio>
#include <iomanip>
#define ll long long
#define rep2(i,a,b) for(int i=a;i<=b;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define rep3(i,a,b) for(int i=a;i>=b;i--)
#define REP(e,v) for(auto e:v)
#define queint queue<int>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pq priority_queue<int>//大きい順
#define pqg priority_queue<int,vec,greater<int>>//小さい順
#define pb push_back
#define vec vector<int>
#define vecvec vector<vector<int>>
#define vecll vector<ll>
#define vecvecll vector<vector<ll>>
#define bs binary_search
#define All(c) (c).begin(),(c).end()
#define mp make_pair
using namespace std;
int in(){int x;scanf("%d",&x);return x;}
string stin(){string s;cin>>s;return s;}
ll lin(){ll x;scanf("%lld",&x);return x;}
int main(){
    int n=in();
    vec a(n);
    rep(i,n){
        a[i]=-in();
    }
    vec q;
    q.pb(a[0]);
    for(int i=1;i<n;i++){
        auto id = upper_bound(All(q),a[i]);
        if(id-q.begin() == q.size()){
            q.pb(a[i]);
        }else{
            q[id-q.begin()]=a[i];
        }
    }
    cout<<q.size()<<endl;
}