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 <iostream>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;

int main(){
	ll N;
	cin >> N;
	vll A(N);
	for(int i=0; i<N; i++){
		cin >> A[i];
	}

	vll maxs(1,-1);
	bool isSmaller;
	for(int i=0; i<N; i++){
		isSmaller=true;
		for(int j=0; j<maxs.size(); j++){
			if(maxs[j]<A[i]){
				maxs[j]=A[i];
				isSmaller=false;
				break;
			}
		}
		if(isSmaller){
			maxs.push_back(A[i]);
		}
	}

	cout << maxs.size() << endl;
	return 0;
}