Amumu is the Sadmummy in League of Legends. He has a skill - Bandage Toss.
Amumu stand at a position and stretch his bandage. If the bandage touches someone, then the one be touched will be caught.

Now EZ is trying to get rid of Amumu's Bandage Toss. He start running at p1(x1, y1), the direction vector is (dx, dy) and his speed is s1 unit per second.
Amumu stand at p2(x2, y2) and he select a direction to stretch his bandage. The maximum length of his bandage is L, and the speed of his stretch is s2 unit per second.

Can you tell Amumu whether he can catch EZ? If he can, you should tell him the earliest time he can catch EZ.

This problem has severel cases. Each case contains nine double.
x1, y1, dx, dy, s1, x2, y2, L, s2

You can consider that at the start point, EZ is out of Amumu's toss area. That means |p1 - p2| > L.

For each case, you should output the earliest time Amumu can catch EZ, two decimal places. If he can't catch EZ, then output 'EZ is lucky~'.