Bricole

Time Limit: 1 Second    Memory Limit: 32768 KB

Bricole is a useful tool in wara. This time, you, as an amateurish soldier, received a command to destroy a goal by bricole. Let us see how high is your rp.

The goal area is between l1 and l2 metres away from the bricole, and the line between the goal and the bricole is horizontal. Because you are not professional, the bricole's elevation is averagely distributed in a region between a1 and a2 (in degrees), and the stone's initial velocity averagely is distributed evenly between v1 and v2 (m/s). Unfortunately, there is a wall of height h (m) ahead, it's l metres away.

Although you are not a good soldier, you are an expert of computer. The question is what's the possibility you can hit the goal.

NOTE: Assume the acceleration of gravity is always 9.8 m/s^2

Input

There are multiple test cases. Each test case is only one line with eight non-negative float number a1, a2, v1, v2, l1, l2, l, h. Proceed to the end of file.

Output

For each test case you just need to output a float number in one line, round to the nearest percent.

Sample Input

0 90 0 100 0 10000000 2 0

Sample Output

1.00

Submit

Source: ZOJ Monthly, February 2005