Grateful Seagull
Seva cherished his hometown of Sevastopol, along with the sea and the seagulls. While walking along the shore, he often fed the seagulls, who recognized him from afar and greeted him with their loud cries.
The seagulls, besides enjoying the sea, Sevastopol, Seva, and his feedings, also loved fish. They were adept at hunting fish, rarely missing their target. Only a young and inexperienced seagull might make a mistake by going after a fish that was too large for its beak or too swift for its wings.
When a fish swam close to the sea's surface, experienced seagulls, like computers, would quickly calculate if they could catch it. If they could, they would fly the shortest path to snatch the fish from the water. The seagulls would also announce their discovery of potential prey with a distinctive cry.
Seva was curious about this: what distance would the fish swim once spotted by the seagull, assuming both the seagull and the fish moved in straight lines during this time? Help Seva find the answer to this intriguing question.
Input
The first line contains 4 numbers separated by spaces: the coordinates of the seagull X_1, Y_1, Z_1, and the magnitude of the seagull's velocity vector V_1. The second line provides the coordinates of the fish's initial position X_2, Y_2, followed by two numbers X_3, Y_3 that specify the magnitude of the fish's speed and direction of movement. All input values are integers and do not exceed 1000 in absolute value. Coordinates are in meters, and speed is in meters per second.
In this problem, consider the seagull and the fish as point masses.
Output
Output a single number representing the answer to Seva's question, with an accuracy of at least 3 decimal places. This means the relative and absolute error of the calculations should not exceed 0.001.
If the seagull catches up with the fish after more than 5 minutes, output -1. If the seagull cannot catch the fish under these conditions, output "You are still young...".