Problem:
Dropping Ink

As shown in the following figure, there is a paper consisting of a grid structure where each cell is indicated by (x, y) coordinate system.

We are going to put drops of ink on the paper. A drop comes in three different sizes: Large, Medium, and Small. From the point of fall, the ink sinks into surrounding cells as shown in the figure depending on its size. In the figure, a star denotes the point of fall and a circle denotes the surrounding cells.

Originally, the paper is white that means for each cell the value of density is 0. The value of density is increased by 1 when the ink sinks into the corresponding cells.

For example, if we put a drop of Small ink at (1, 2) and a drop of Medium ink at (3, 2), the ink will sink as shown in the following figure (left side):

In the figure, density values of empty cells are 0. The ink sinking into out of the paper should be ignored as shown in the figure (top side). We can put several drops of ink at the same point.

Your task is to write a program which reads a sequence of points of fall (x, y) with its size (Small = 1, Medium = 2, Large = 3), and prints the number of cells whose density value is 0. The program must also print the maximum value of density.

You may assume that the paper always consists of 10 × 10, and 0 ≤ x < 10, 0 ≤ y < 10.

Input

x1,y1,s1
x2,y2,s2
:
:

(xi, yi) represents the position of the i-th drop and si denotes its size. The number of drops is less than or equal to 50.

Output

Print the number of cells whose density value is 0 in first line.

Print the maximum value of density in the second line.

Sample Input

2,5,3
3,6,1
3,4,2
4,5,2
3,6,3
2,4,1

Output for the Sample Input

77
5

Solution in Ruby (judge verdict: Accepted)

class Square
  attr_reader :squares

  def initialize
    @squares = build_two_dimensions
  end

  def build_two_dimensions
    Array.new(10) { [] }.map { Array.new(10) { 0 } }
  end

  def update(x, y, size)
    range = case size
            when 1
              small_range
            when 2
              middle_range
            when 3
              large_range
            else
              []
            end

    range.each do |a, b|
      increment(x + a, y + b)
    end
  end

  def zero_count
    squares.flatten.select(&:zero?).count
  end

  def max
    squares.flatten.max
  end

  private

  def large_range
    middle_range.concat [[-2, 0], [0, -2], [0, 2], [2, 0]]
  end

  def middle_range
    small_range.concat [[-1, -1], [-1, 1], [1, -1], [1, 1]]
  end

  def small_range
    [[-1, 0], [0, -1], [0, 0], [0, 1], [1, 0]]
  end

  def increment(x, y)
    squares[x][y] += 1 if x.between?(0, 9) && y.between?(0, 9)
  end
end

square = Square.new
STDIN.read.split("\n").each do |line|
  x, y, size = line.split(',').map(&:to_i)
  square.update(x, y, size)
end
puts [square.zero_count, square.max]