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 <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <string>
#include <iomanip>
#include <map>
#include <set>
#include <cmath>
#include <cstdio>
using namespace std;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define FOR(i,m,n) for(int (i)=(m);(i)<(n);(i)++)
#define All(v) (v).begin(),(v).end()
typedef long long ll;

int main(){
    int N;cin >> N;
    vector<int> A(N);
    rep(i,N)cin >> A[i];
    multiset<int> se;
    se.insert(A[0]);
    for(int i=1;i<N;i++){
        auto ite = se.lower_bound(A[i]);
        if(ite==se.begin()){
            se.insert(A[i]);
        }else{
            ite--;
            se.erase(ite);
            se.insert(A[i]);
        }
    }
    //for(auto x:se)cout << x << endl;
    cout << se.size()<< endl;
    return 0;
}