Problem B
Framhjá Polli

Jörmunrekur needs to get from one place to another, but he’s not quite sure how long it’ll take him. He might not be able to walk directly between those end points since there is a large puddle he can’t step into. As we all know puddles are perfectly circular. We have his initial and desired final position, along with the size and location of the puddle. Can you figure out how far he has to walk?

Input

The input starts with four floating point numbers $-{10}^9\le x_1,y_1,x_2,y_2\le {10}^9$. $(x_1,y_1)$ denotes Jörmunrekur’s initial position and $(x_2,y_2)$ denotes his desired final position. Next there is a line with three floating point values $-{10}^9\le x_p,y_p,r\le {10}^9$ where $(x_p,y_p)$ denotes the centre of the puddle and $r$ its radius. Neither the starting position nor the desired final position will be in the puddle. All floating point numbers in the input have at most $6$ digits after the decimal.

Output

Print the distance Jörmunrekur has to travel in the best case if he’s not allowed to step in the puddle. The answer is considered correct if the absolute or relative error is at most ${10}^{-5}$ with respect to the correct answer.

8 10 2 2
5 6 1.5

10.45346997

10 10 -10 10
0 0 8

20.0

-3 -3 12 4
0 0 4

17.77046301