Pair Sum

Given a natural number $n$ with $1 \le n \le 12$, write a program that finds every pair of two distinct natural numbers whose sum is $n$.

Each pair has the form $(a, b)$, where the two numbers must be different (for example, $3$ and $3$ is not a valid pair) and the first number must always be smaller than the second one ($a < b$).

Print the pairs in lexicographic order, comparing by the smaller number (the first number) of each pair. For example, $(1, 5)$ comes before $(2, 4)$.

The first line contains the number of test cases $T$ ($T < 100$). Each of the next $T$ lines contains one natural number $n$ ($1 \le n \le 12$).

For each test case, first print Pairs for n: (where n is the actual value). Then, after a single space, print the pairs whose sum is $n$ in lexicographic order, separated by , (a comma and a space). Each pair is printed as a b, its two numbers separated by a single space. If there is no pair that sums to $n$, print nothing after Pairs for n:.