Love Story I

Time Limit: 1000 ms

Memory Limit: 65535 ms

Description

Once upon, there was a famous couple between on earth, just because the girl was a fairy coming from the sky and the boy was just a farmer whose unique property was an old bull. A talented poet had written a poem for them, saying that,” Clouds float like works of art. Stars shoot with grief at heart. Across the Milky Way, the cowherd meets the maid, when autumn’s golden wind embraces dew of jade. All the love scenes on earth, however many fade. Their tender love flows like a stream. This happy date seems but a dream. Can they bear a separate homeward way? If love between both sides can last for age, why need they stay together night and day?”
Even though the boy’s mother-in-law was extremely cruel, she reluctantly allowed her daughter and her son-in-low meeting once in one year along the Milky Way. The boy was perturbed and moved between two locations in a straight line, back and forth at a fixed speed. The girl was eager to see her husband, so she would pick the straightway road which is a line and fly to her sweetheart at a maximal speed. Now they wanted to know whether they could have a date successfully. If their minimal distance was longer than their eyesight distance, they would miss each other, so it’s your job to calculate their minimal distance. Be careful that they started at the same time.

Input

Input contains multiple test cases. Each test case contains two lines in the following format. bx1 by1 bx2 by2 bv gx1 gy1 gx2 gy2 gv (bx1, by1) means the start position of the boy, (bx2, by2) is another position of the line, and bv is his speed. (gx1, gy1) and (gx2, gy2) won’t be the same at one time. (gx1, gy1) is the start position of the girl and (gx2, gy2) is one point on her direction, and gv is her speed. All numbers in the input are floating numbers.(-500000000 <= bx1, by1, bx2, by2, gx1, gy1, gx2, gy2 <= 500000000, 0 <= bv, gv <= 20000)

Output

For each case just output one line contains the minimal distance in exactly 5 digits.

Sample Input

-5002 2349.1 23434.234 234 4
-238 0 341 13 43

Sample Output

5311.68211

Hint

Source

方静远

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