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)

parseInt(x)=parse(Int,x)
parseMap(x::Array{SubString{String},1})=map(parseInt,x)
function bsearchg(a,x);l,r=1,length(a);while l<=r;m=r-div(r-l,2);if a[m]>x;r=m-1;else;l=m+1;end;end;return(l-1);end

function main()
	n = readline() |> parseInt
	a = Array{Int}(n)
	for i in 1:n
		a[i] = readline() |> parseInt
	end
	k = 1
	ma = a[n]
	stack=Int[a[n]]
	for i in 1:n-1
		x = bsearchg(stack,a[n-i])
		if x<length(stack)
			stack[x+1] = a[n-i]
		else
			push!(stack,a[n-i])
		end
	end
	println(length(stack))
end

main()