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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.chomp.to_i
a = Array.new(1,10**9+1)
color = 0
left = 0
right = 0
center = 0
for i in 1..N do
    x = gets.chomp.to_i
    if x <= a[color]
        a.push(x)
        color += 1
    else
        left = 0
        right = color
        while left != right
            center = (left+right)/2
            if a[center] < x
                right = center
            elsif
                left = center+1
            end
        end
        a[left] = x
    end
end
puts color