There is a car, a bus, and a truck moving in the same direction on an infinite road. The road has two lanes labeled Lane 1 and Lane 2. The bus will keep moving forward staying on Lane 1 with a constant speed S_B meters per second and the car will keep moving forward staying on Lane 2 with a constant speed S_C meters per second. They will not change their lanes or speeds. The length of the bus is L_B meters and it is D_B meters ahead of the truck. The length of the car is L_C meters and it is D_C meters ahead of the truck. The length of the truck is L_T meters and the maximum speed of the truck is S_T meters per second.

The truck wants to overtake both of the vehicles without any accidents. The truck will overtake the car, if it is at least L_T meters ahead of the car. Similarly, the truck will overtake the bus, if it is at least L_T meters ahead of the bus.

If the truck is driven on lane 1, the truck must stay at least L_B meters behind the bus or at least L_T meters ahead of the bus to avoid an accident with the bus. Similarly, if the truck is driven on lane 2, the truck must stay at least L_C meters behind the car or at least L_T meters ahead of the car to avoid an accident with the car.

You may safely assume:

1. No accident has occurred till now.
2. The truck is either on lane 1 or lane 2, we do not know. The truck driver can instantly change between lane 1 and lane 2.
3. The truck driver can instantly change its current speed to any value between 0 to S_T meters per second.
4. Each lane contains sufficient space for only one vehicle and at any particular moment the truck will be driven either on lane 1 or lane 2.

You are given all the information, you have to find out the minimum amount of time the truck will take to overtake both of the vehicles.

First line of the input file contains a positive integer T (T ≤ 100000) which denotes the number of test cases to follow.

Each of the next T test cases contains three lines of inputs. The first line of the test case contains three space-separated integers L_B (1 ≤ L_B ≤100), S_B (1 ≤ S_B ≤100), and D_B (1 ≤ D_B ≤1000). The next line contains three space-separated integers L_C (1 ≤ L_C ≤100), S_C (1 ≤ S_C ≤100), and D_C (1 ≤ D_C ≤1000). The last line of the case contains two space-separated integers L_T (1 ≤ L_T ≤100) and S_T (1 ≤ S_T ≤100).

You may safely assume that L_C≤ D_C or L_B ≤ D_B or both are valid.

For each case, print Case t: x, where t is the test case number and x is the minimum time to overtake both of the vehicles rounded up to four digits after decimal points. If it is impossible to overtake both vehicles, then print -1 instead.

Large I/O, Avoid endl with cout.