You are given a 3D grid, which have dimensions N, M and P. Each of the M ×N ×P cells has a light. Initially all lights are off. You will have K turns. In each of the K turns, • You will select a cell A randomly from the grid • You will select a cell B randomly from the grid • Toggle the states of all the bulbs bounded by cell A and cell B, ie make all the ON lights OFF and make all the OFF lights ON which are bounded by A and B. To be more 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). How many bulbs are expected to be ON after K turns? Note: A and B can be the same cell. Input First line of the input is an integer T (T < 101) which denotes the number of test cases. Each of the next T lines represents one test case by 4 integers N, M, P (0 < M,N,P < 101) and K (0 ≤ K ≤ 10000) separated by spaces. Output Output one line for each test cases giving the expected number of ON lights. Up to 1E-6 error in your output will be acceptable. Print the case number followed by the output. Look at the sample output for exact format. Sample Input 2 2341 2342 Sample Output Case 1: 6.3750000000 Case 2: 9.0976562500