I. B'obr
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You were flying in an airplane over the Vitebsk region and suddenly realized that you missed the beaver. You jumped out of the plane with a parachute and landed at point $$$A = (x_1, y_1)$$$, knowing for sure that your faithful friend the beaver is at point $$$B = (x_2, y_2)$$$.

There is also a lake in the forest, which is a circle with radius $$$r$$$, centered at the origin $$$(0, 0)$$$. You can move to any point in the forest (including swimming across the lake) at a speed of $$$1$$$, while along the lake, the beaver has built a dam, which allows you to move at a speed of $$$v$$$.

You are interested in the minimum amount of time it will take you to reach the beaver.

Input

The first line contains the number $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case is described by a single line containing the integers $$$x_1$$$, $$$y_1$$$, $$$x_2$$$, $$$y_2$$$, $$$r$$$, and $$$v$$$ ($$$|x_i|, |y_i| \le 10^9$$$, $$$1 \le r, v \le 10^9$$$). It is guaranteed that $$$x_1^2 + y_1^2 \ge r^2$$$ and $$$x_2^2 + y_2^2 \ge r^2$$$.

Output

For each test case, output a single number — the minimum time it takes to reach the beaver.

The answer will be considered correct if the relative or absolute error does not exceed $$$10^{-6}$$$.

Example
Input
3
-4 0 4 0 3 3
-4 0 4 0 3 1000000000
-1 10 1 10 8 1000
Output
5.056391787888
2.000000009425
2.000000000000