Glide Reflection

A motion is a transformation of the plane that preserves distances between points: if a motion sends points $A$ and $B$ to $A_1$ and $B_1$, then $|A_1B_1| = |AB|$.

One kind of motion is a glide reflection. A glide reflection is the composition of a reflection across some line $l$ and a translation by a vector parallel to $l$ (the vector may be zero). The figure shows a glide reflection applied to a segment.

A FIGURE GOES HERE

It is known that any segment can be mapped to any other segment of the same length by a glide reflection.

Given the coordinates of two distinct points $A$ and $B$ and of two points $A_1$ and $B_1$ that are the same distance apart, find a glide reflection that sends $A$ to $A_1$ and $B$ to $B_1$.

The first line contains four integers: the coordinates of two distinct points $A$ and $B$. The second line also contains four integers: the coordinates of two distinct points $A_1$ and $B_1$. It is guaranteed that $|A_1B_1| = |AB|$. Every number in the input has absolute value at most 1000.

Print a description of the glide reflection you found.

On the first line print the coordinates of two distinct points lying on the line $l$ of the reflection, and on the second line print the coordinates of the translation vector parallel to that line. Print real numbers with at least 6 digits after the decimal point.