Anna University Local Contest #10

OMG is crazy about geometrical shapes. She creates random geometrical figures in her mind and starts to study them. Now, OMG has two non intersecting circles. Also one circle is not inside another. She plots 4 points, 2 in each circle's circumference. Then she connects the 4 points using 3 straight lines with the condition that none of the lines intersect the circles. By this formation, she wonders what the maximum total length of the connected lines will be. Can you help her?

Here is an example for a vaild formation(but not optimal)

Input

First line contains T, the number of test cases.

Next T lines contain 6 integers: r1 x1 y1 r2 x2 y2

r1, r2 are radii of the circles

(x1, y1), (x2, y2)  are the centres of the circlles.

Output

For each test case the maximim length possible(accurate to 10e-6)

Constraints

1 <= T <= 1000;

-100000 <= x1, y1, x2, y1 <= 100000

1 <= r1 <= 100000

Example

Input:
3
3 0 -5 3 0 5
3 0 -5 2 0 5
1 -1000 -1000 1 1000 1000

Output:
22.000000
19.949874
2832.427125

No explanations!