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<bits/stdc++.h>
using namespace std;
vector<int> v;
int n,ans=0;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		int x;
		cin>>x;
		if(v.empty())
		{
			v.push_back(x);
			++ans; 
		} 
		else
		{
			if(x<=v[0])
			{
				v.insert(v.begin(),x);
				++ans;
			}
			else
			{
				int tmp=lower_bound(v.begin(),v.end(),x)-v.begin()-1;
				v.erase(v.begin()+tmp);
				v.insert(v.begin()+tmp,x);
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}