Bob wants to pour water

Time Limit: 2 Seconds

Memory Limit: 65536 KB

Description

There is a huge cubiod house with infinite height. And there are some spheres and some cuboids in the house. They do not intersect with others and the house. The space inside the house and outside the cuboids and the spheres can contain water.

Bob wants to know when he pours some water into this house, what's the height of the water level based on the house's undersurface.

Input

The first line is a integer T (1 ≤ T ≤ 50), the number of cases.

For each case:

The first line contains 3 floats w, l (0 < w, l < 100000), the width and length of the house, v (0 < v < 1013), the volume of the poured water, and 2 integers, m (1 ≤ m ≤ 100000), the number of the cuboids, n (1 ≤ n ≤ 100000), the number of the spheres.

The next m lines describe the position and the size of the cuboids.

Each line contains z (0 < z < 100000), the height of the center of each cuboid, a (0 < a < w), b (0 < b < l), c, the width, length, height of each cuboid.

The next n lines describe the position and the size of the spheres, all these numbers are double.

Each line contains z (0 < z < 100000), the height of the center of each sphere, r (0 < 2r < w and 2r < l), the radius of each sphere.

Output

For each case, output the height of the water level in a single line. An answer with absolute error less than 1e-4 or relative error less than 1e-6 will be accepted. There're T lines in total.

Sample Input

1
1 1 1 1 1
1.5 0.2 0.3 0.4
0.5 0.5

Sample Output

1.537869

Hint

None

Source

None

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