# Problem H

# HARDLY HARD

You have been given the task of cutting out a quadrilateral slice of cake out
of a larger, rectangular cake. You must find the slice with the smallest
perimeter that satisfies the following constraints.
If the cake is of size 10000-by-10000 units and is represented using the first
quadrant of the Cartesian plane, then your slice is quadrilateral ABCD (see figure).
Points A and B are fixed and will be given to you. Also, A,B will lie on a negatively sloping line.
Furthermore, points C and D must lie on the positive y-axis and positive x-axis
respectively, but it is up to you to determine where these two points should be.
A,B,C,D will be distinct points.

Output the minimum perimeter of your slice of cake.

## Input

On the first line you will be given *n* (1 ≤ *n* ≤ 100),
the number of test cases. The following *n* lines each contain
*ax ay bx by* (0 < *ax, ay, bx, by* ≤ 10000.0),
the coordinates of points A and B respectively.

## Output

For each test case, output the perimeter accurate to 3 decimal places on
its own line.

## Sample Input

1
3.0 1.0 1.0 2.0

## Output for the Sample Input

7.236

*John Zhang*

*Calgary Collegiate Programming Contest 2007*