Mr. J wants to learn about combinatorics. He started reading a book on combinatorics and came across this problem:
A town, rectangular in shape, has a grid-like street network. It consists of x+1 parallel lines headed north-south and y+1 parallel lines headed east-west. You can think of Manhattan as an example. In how many ways can a car reach the north-east corner if it starts in the south-west comer and travels only in the east and north directions?"
So the problem is, you are at position in a grid. You can only go to the right or towards the top. You have to determine, how many ways you can go to .
Now Mr. J found the solution of the problem in the book, and he started to wonder what if he adds a third dimension to this problem.
Imagine there is a box with width, height and depth. You are standing in one corner . In each move, you can only go front (+1 in X dimension), right (+1 in Y dimension) and towards the top (+1 in Z dimension). So from you can go to , , or in one move.
Now determine how many ways you can go to the corner from . Two ways are considered different if after any one of the moves they are in a different position in the box.
The first line of the input is (), the number of test cases. Then test cases follow.
Each test case has 3 integers , , () in a line. They represent the width, the height and the depth of the box respectively.
For each test case, print a line in "Case #K: R" format where K is the case number and R is the desired result.
3 1 1 1 1 1 2 2 1 1
Case #1: 6 Case #2: 12 Case #3: 12