Block pathing

You are an ant on a childs toy, and would like to find the shortest path between two points. The childs toy simply contains two objects: An axis-aligned rectangle and a circle.

You can assume that:

• The two objects don't overlap
• The two objects don't "kiss" (there is a non-zero distance between the two)

What is the shortest distance from start to finish?

Input

Input will always have the same number of values, all of which are integers, in the following form:

sx sy
ex ey
blx bly trx try
rad cx cy

Where:

• sx and sy are the x/y coordinates of the starting position
• ex and ey are the x/y coordinates of the end goal
• blx and bly are the x/y coordinates of the bottom left corner of the rectangle
• trx and try are the x/y coordinates of the top right corner of the rectangle
• rad is the radius of the circle
• cx and cy are the x/y coordinates of the centre of the circle

Output

Output a single value representing the shortest distance from the start to end goal. Any answer with absolute or relative error of ~10^{-6}~ will be considered correct.

Example

Take the following input:

1 1
14 14
2 2 7 7
4 11 11

This is represented by the following graph:

Which can be pathed in the following manner:

Resulting in a distance of

21.625015745078453

Constraints

• All values given are in the range ~[0, 10^9]~