752. The Champion's Cup

0

Medium

Martin is diligently preparing for the prestigious Champion's Cup. The race will take place from point A to point B, with point A located on the ground and point B situated in the sea. The race arena is represented by a two-dimensional plane. The coordinates of point A and point B are given as (x1, y1) and (x2, y2) respectively. The ground section is defined as the area below the line y = 0, the coastline is represented by the line y = 0, and the sea section is the area above the line y = 0. Martin's speed on the ground is v1, and his swimming speed is v2. Assist Martin in determining the minimum time required to complete the race.

Input Format

The first line contains a single integer T, denoting the number of test cases. Each of the following T lines contains 6 space-separated integers: x1, y1, x2, y2, v1, and v2.

Output Format

For each test case, output the minimum time required with exactly 5 digits after the decimal point.

Example

Input

1 3 -20 3 25 40 5

Output

5.50000

Constraints

1 <= T <= 100
-109 <= x1 ,x2 <= 109
-109 <= y1 < 0
0 < y2, v1, v2 <= 109