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: Runtime Error)

n = gets.chomp.to_i
stack = []
# min = Float::INFINITY
for i in 1..n do 
    a = gets.chomp.to_i
    # if min >= a
    #     stack.push(a)
    #     min = a
    # else
        head = 0
        tail = (stack.size) -1
        mid = (head+tail)/2
        
        while head < tail
            if stack[mid] > a
                head = mid+1
            else
                tail = mid-1
            end
            mid = (head+tail)/2
        end
        stack[mid] = a
    end
end

p stack.size