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: Wrong Answer)

n = gets.chomp.to_i
stack = []
for i in 1..n do 
    a = gets.chomp.to_i
    if stack.empty?
        stack.push(a)
        next
    end
    head = 0
    tail = (stack.size) -1
    mid = (head+tail)/2
    
    if stack[tail] > a
        stack.push(a)
        next
    end

    while head < tail
        if stack[mid] > a
            head = mid+1
        else
            tail = mid-1
        end
        mid = (head+tail)/2
    end

    stack[mid] = a
end

p stack.size