You are given a 3D grid, which has dimensions X, Y and Z. Each of the X x Y x Z cells contains a light. Initially all lights are off. You will have K turns. In each of the K turns,
- You select a cell A randomly from the grid,
- You select a cell B randomly from the grid and
- Toggle the states of all the bulbs bounded by cell A and cell B, i.e. make all the
ONlightsOFFand make all theOFFlightsONwhich are bounded by A and B. To be clear, consider cell A is (x1, y1, z1) and cell B is (x2, y2, z2). Then you have to toggle all the bulbs in grid cell (x, y, z) where min(x1, x2) ≤ x ≤ max(x1, x2), min(y1, y2) ≤ y ≤ max(y1, y2) and min(z1, z2) ≤ z ≤ max(z1, z2).
Your task is to find the expected number of lights to be ON after K turns.
Input
Input starts with an integer T (≤ 50), denoting the number of test cases.
Each case starts with a line containing four integers X, Y, Z (1 ≤ X, Y, Z ≤ 100) and K (0 ≤ K ≤ 10000).
Output
For each case, print the case number and the expected number of lights that are ON after K turns. Errors less than 10-6 will be ignored.
Sample
| Sample Input | Sample Output |
|---|---|
5 1 2 3 5 1 1 1 1 1 2 3 0 2 3 4 1 2 3 4 2 | Case 1: 2.9998713992 Case 2: 1 Case 3: 0 Case 4: 6.375 Case 5: 9.09765625 |