More Dice

You roll two standard six-sided dice. Given the sum of the roll, find every combination of die values that produces that sum. Combinations that differ only in order count as the same combination, so (1,6) and (6,1) are the same one and only one of them is listed.

The first line contains the number of test cases.

Each test case is one line holding a single integer. The value is the sum of a roll of two six-sided dice, so it is between 2 and 12.

There are at most 1000 test cases.

For each test case, first print Case x: on a line of its own, where x is the case number counting from 1.

Then print the pairs of die values that add up to that sum, one per line. Each pair has its two values separated by a comma and wrapped in parentheses, and inside a pair the smaller value comes first. Print the pairs in increasing order of the smaller die.