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Background

Drew: Hey, are you gonna go to the tour on Sunday?

Taylor: Oh, I was thinking about it. Why?

Drew: Oh, I don't know. Just asking.

Drew: Oh, I met this girl. I gonna tell you about it later.

(Taylor exhales deeply) (gentle wistful music)

Description

Drew and Taylor was visiting Anhui's Celebrities Museum(安徽省名人馆)on 16th, April, 2023. As the standard-bearer of the class, Taylor was stopped by the gatekeeper because her flag was too long to carry into the museum. It takes her some time to put flagstaff away. When she finally came in, It was sad for her to miss the trace of Drew.

Fortunately, Yang, a friend of Taylor, was visiting the museum side by side with Drew. He had told the coordinate, direction vector and the speed of them. Taylor wanted to know how long it will take to catch up with Drew if she run to the optimum direction as far as she can.

• Assuming the museum has only one floor, we can consider it as a two-dimensional surface and represent the coordinates with a two-dimensional point and the direction of movement with a two-dimensional vector. So we define Taylor started at $(0, 0)$ with a speed of $v_t$. Drew and Yang started at $(x_d, y_d)$, and had a traveling speed of $v_d$ with a direction vector of $(m, n)$.
• Assuming Drew and Yang's original positions are $(x, y)$,
  after $t$ seconds, their positions will be $(x + t \times m \times v_d, y + t \times n \times v_d)$.
• Assuming the museum is infinitely large, without considering the boundaries of the museum.
• Assuming we can freely move within the library, without considering the walls or exhibits inside the museum.

Format

Input

6 decimal numbers $v_t,\ x_d,\ y_d,\ m,\ n,\ v_d$, represent Taylor's speed, Drew and Yang's starting point, Direction vector of their movement and their speed.

It is guaranteed that $-10^6 \le x_t, x_d, y_d, m, n, v_d \le 10^6$.

All the decimal numbers are rounded to no greater than 3 decimal places.

Output

• If Taylor can't catch up with Drew within $10^9$ seconds, Please output a single line Drew, Please wait for me!
• If Taylor can catch up with Drew within $10^9$ seconds, output a decimal number $t$, represent the minimum time required for Taylor to catch up with Drew. Please rounded your output to 5 decimal places, because only when your output is exactly same to the standard answer will it be accepted.

Sample

4 5 0 -0.6 0.8 3

1.00000

3.464 1 0 0.5 0.866 2

0.50002

Limitation

1s, 128MB

Drew walks by me
Can he tell that I can't breathe?
And there he goes, so perfectly
The kind of flawless I wish I could be.