Two trains P90619

Consider two infinite horizontal train rails, so close that we can regard them to be coincident. On the first rail there is a train of length $\ell_1$. To its right, on the second rail and $d$ distance units apart, there is a train of length $\ell_2$. This simple picture corresponds to all the cases of the sample input, with $\ell_1 = 10$, $\ell_2 = 20$ and $d = 30$:

The first train has velocity $v_1$ and constant acceleration $a_1$. The second train has velocity $v_2$ and constant acceleration $a_2$. Positive means to the right, negative means to the left. For how many time units will the trains overlap, at least partially?

Input

Input consists of several cases, with only integer numbers, each one with $\ell_1$, $\ell_2$, $d$, $v_1$, $a_1$, $v_2$ and $a_2$. Assume that $\ell_1$, $\ell_2$ and $d$ are strictly positive. No number is larger than $10^4$ in absolute value.

Output

For every case, print with four digits after the decimal point the amount of time that both trains will overlap. The input cases have no precision issues.