Football
This problem will be submitted in the 90th minute of the contest.
Octopus Paul
In the football team "Oranges," there are four forwards. The football team "Berries" has several defenders and a coach who insists that on the line segment connecting any two forwards from the opposing team, there must be at least one defender to intercept the ball if a pass is made.
You are given the current positions of the forwards on the field. Your task is to position the minimum number of defenders such that the coach's requirement is met.
No two players can occupy the same position.
Input
The input consists of four pairs of integers, each pair on a separate line, representing the coordinates of the forwards. The coordinates do not exceed 100 in absolute value.
Output
On the first line of the output, print n - the minimum number of defenders required to intercept all possible passes between the "Oranges" forwards.
In the following n lines, print pairs of real numbers representing the coordinates of the defenders, with a precision of at least 5 decimal places.
If there are multiple valid solutions, you may output any one of them.