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 <cstdio>
int f[1000001],a[1000001];
int main()
{
	int ans=0,n=0;
	scanf("%d",&n);
	for (int i=1;i<=n;++i)	scanf("%d",&a[i]);
	f[0]=-1,ans=0;
	for(int i=n;i>=1;--i){
		if(f[ans]<=a[i])	f[++ans]=a[i];
		else{
			int l=0,r=ans;
			while(l<r){
				int mid=(l+r)/2;
				if(f[mid]>a[i])	r=mid;
				else	l=mid+1;
			}
			f[l]=a[i];
		}
	}
	printf("%d",ans);
	return 0;
}