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 Julia (0.5.0) (judge verdict: Accepted)

N=parse(Int,readline())
K=-ones(Int,N)
for _=1:N
	A=parse(Int,readline())
	L=0
	R=N
	while R-L>1
		M=div(L+R,2)
		if K[M]<A
			R=M
		else
			L=M
		end
	end
	K[R]=A
end
id=1
while id<N&&K[id+1]>=0
	id+=1
end
println(id)