I	Collision of Bacteria

An experiment is being conducted to find out how different colonies of bacteria behave when they collide with each other. The individual colonies are placed on a large dish and the dish can be modeled in a 2D plane. Initially, each colony occupies a rectangular area (sides parallel to axis) and the sizes of these colonies grow with time. The growth of the colonies occurs in the following manner:

1. The x and y coordinate of the lower-left corner decrease.

2. The x coordinate of lower-right corner increases and the y coordinate decreases.

3. The x and y coordinate of upper-right corner increase.

4. The x coordinate of upper-left corner decreases and the y coordinate increases.

All the increments/decrements mentioned above occur at a constant rate r with respect to time. In this problem, you have to determine the smallest unit of time that elapses when there are at least two colonies that are not more than d distance apart. Here the distance refers to the shortest Euclidean distance between the rectangular areas occupied by the colonies.

Input

The first line of input will contain T (≤ 100) denoting the number of cases.

Each case starts with an integer n (2 ≤ n ≤ 50) denoting the number of colonies. Each of the next n lines contains 4 integers x₁ y₁ x₂ y₂ (0 ≤ x₁, y₁, x₂, y₂ ≤ 10000, x₁ < x₂, y₁ < y₂) where (x₁, y₁) and (x₂, y₂) denote the lower-left and upper-right corner of the colony respectively. Next line contains two integers, r and d (1 ≤ r, d ≤ 50).

Output

For each case, print the case number and the desired result rounded to 3 places after the decimal point. If two colonies overlap or just touch each other, they are considered to be zero distance apart.

Sample Input	Output for Sample Input
2 2 0 0 1 1 3 0 4 1 1 1 2 0 0 1 1 0 1 3 2 1 1	Case 1: 0.500 Case 2: 0.000

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Problem Setter: Shamim Hafiz, Special Thanks: Tanaeem M Moosa, Jane Alam Jan