Description

Original Source: SCOI 2010

On a two-dimensional plane, there are two conveyor belts, each of which can be considered as a line segment. The two conveyor belts are segments $\text{AB}$ and $\text{CD}$ respectively. lxhgww moves at speed $P$ on $\text{AB}$, at speed $Q$ on $\text{CD}$, and at speed $R$ elsewhere on the plane.

Now, lxhgww wants to travel from point $A$ to point $D$ and wishes to know the minimum time required.

Input Format

The first line of input contains four integers representing the coordinates of $A$ and $B$, namely $A_x, A_y, B_x, B_y$;

The second line contains four integers representing the coordinates of $C$ and $D$, namely $C_x, C_y, D_x, D_y$;

The third line contains three integers, $P, Q, R$.

Output Format

The output consists of a single line, displaying the shortest time for lxhgww to travel from point $A$ to point $D$, rounded to two decimal places.

Sample 1

0 0 0 100
100 0 100 100
2 2 1

136.60

Data Range and Hint

For $100\%$ of the data, $1 \leq A_x, A_y, B_x, B_y, C_x, C_y, D_x, D_y \leq 1000$, and $1 \leq P, Q, R \leq 10$.