359. 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 land 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 land portion is defined as the area below the line**y = 0**, the coastline is represented by the line**y = 0**, and the sea portion is the area above the line**y = 0**. Martin's speed on land 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. The following T lines each contain 6 space-separated integers: x1, y1, x2, y2, v1, and v2.

Output Format

For each test case, output the minimum time required, rounded to exactly 5 decimal places.

Example

Input

1
3 -20 3 25 40 5

Output

5.50000

Constraints

1 <= T <= 100

-10^{9} <= x1 ,x2 <= 10^{9}

-10^{9} <= y1 < 0

0 < y2, v1, v2 <= 10^{9}

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