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;
#define SORT(x) sort(x.begin(),x.end())
#define ALL(x) x.begin(),x.end()
#define rep(i,n) for(int i=0;i<n;i++)
#define INF 1000000000
#define mod 1000000007
typedef long long ll;
const ll LINF = 1001002003004005006ll;
int dx[]={1,0,-1,0};
int dy[]={0,1,0,-1};
#define No cout<<"No"<<endl
#define Yes cout<<"Yes"<<endl
#define NO cout<<"NO"<<endl
#define YES cout<<"YES"<<endl;
int gcd(int a,int b){return b?gcd(b,a%b):a;}
ll n;
vector<ll> a;
int main(){
    cin>>n;
    a.resize(n);
    rep(i,n){
        cin>>a[i];
    }
    multiset<ll> s;
    s.insert(a[0]);
    for(ll i=1;i<n;i++){
        if(*s.begin()>=a[i]){
            s.emplace(a[i]);continue;
        }
        auto ind=lower_bound(ALL(s),a[i]);
        if(ind==s.begin()){
            s.insert(a[i]);
        }
        else{
            ind--;
            s.erase(ind);
            //eraseをイテレータで消す。→O(1)
            //インデックスでは消せない。
            //int値とかを引数にするとその値を探して消しちゃう
            s.insert(a[i]);
        }
    }
    cout<<s.size()<<endl;
    return 0;
}