Problem:
Score : 300 points

Problem Statement

There is a rectangle in a coordinate plane. The coordinates of the four vertices are (0,0), (W,0), (W,H), and (0,H).
You are given a point (x,y) which is within the rectangle or on its border. We will draw a straight line passing through (x,y) to cut the rectangle into two parts. Find the maximum possible area of the part whose area is not larger than that of the other. Additionally, determine if there are multiple ways to cut the rectangle and achieve that maximum.

Constraints

1 \leq W,H \leq 10^9

0\leq x\leq W

0\leq y\leq H

All values in input are integers.

Input

Input is given from Standard Input in the following format:

W H x y

Output

Print the maximum possible area of the part whose area is not larger than that of the other, followed by 1 if there are multiple ways to cut the rectangle and achieve that maximum, and 0 otherwise.

The area printed will be judged correct when its absolute or relative error is at most 10^{-9}.

Sample Input 1

2 3 1 2

Sample Output 1

3.000000 0

The line x=1 gives the optimal cut, and no other line does.

Sample Input 2

2 2 1 1

Sample Output 2

2.000000 1

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

width,height,x,y=gets.chomp.split(" ").map(&:to_i)

box_area = width * height

max_area = 0.0
multiple = 0

x_cut_left_area = x * height
x_cut_right_area = box_area - x_cut_left_area

x_cut_min_area = x_cut_right_area
if x_cut_left_area < x_cut_right_area
    x_cut_min_area = x_cut_left_area
end

y_cut_top_area = y * width
y_cut_bottom_area = box_area - y_cut_top_area
y_cut_min_area = y_cut_top_area
if y_cut_bottom_area < y_cut_top_area
    y_cut_min_area = y_cut_bottom_area
end

if (x_cut_min_area - y_cut_min_area).abs < 0.00000001
    multiple = 1
end

max_area = x_cut_min_area

if y_cut_min_area > x_cut_min_area
    max_area = y_cut_min_area
end


print("%.8f " %  "#{max_area.to_s}")
print("#{multiple}")