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;

int main(){
	int N;
	cin >> N;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	int ans=1;
	vector<int> m;
	m.push_back(A[0]);
	
	for(int i=1;i<N;i++){
		sort(m.begin(),m.end());
		auto it=lower_bound(m.begin(),m.end(),A[i]);
		if(it==m.begin()){
			ans++;
			m.push_back(A[i]);
		}
		else{
			it--;
			*it=A[i];
		}
	}
	cout << ans << endl;
	return 0;
}