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.to_i
$a = Array.new($n) {
    gets.to_i
}

$x = []
$count_set = 0
$min_count = $n
def solve(j)
    if j >= $n then
        if $min_count > $count_set then
            $min_count = $count_set
        end
        return
    end
    for i in 0...$count_set
        if $x[i][-1] < $a[j] then
            $x[i].push($a[j])
            solve(j + 1)
            $x[i].pop
        end
    end
    $x.push([$a[j]])
    $count_set += 1
    solve(j + 1)
    $x.pop
    $count_set -= 1
end

solve(0)
puts $min_count