Migrated from Lutece 78 Farey Sequence

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Description

The Farey Sequence $F_n$ for any integer $n$ with $n \geq 2$ is the set of irreducible rational numbers $\frac{a}{b}$ with $0 < a < b \leq n$ and $\gcd(a,b) = 1$ arranged in increasing order.

The first few are:

• $F_2 = [\frac{1}{2}]$
• $F_3 = [\frac{1}{3}, \frac{1}{2}, \frac{2}{3}]$
• $F_4 = [\frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}]$
• $F_5 = [\frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}]$

Now, your task is to print Farey Sequence given the value of $n$.

Input

There are several test cases. The first line is an integer giving the number of cases. Each test case has only one line, which contains a positive integer $n$ ($2 \leq n \leq 3000$).

Output

For each test case, you should output one line, which contains the corresponding Farey Sequence. Adjacent terms are separated by a single , and there can't be any white spaces in your output. See Sample Output for more clarifications on the output format.

Samples

4
2
3
4
5

1/2
1/3,1/2,2/3
1/4,1/3,1/2,2/3,3/4
1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5

Note

Do Not use cout to produce the output for this problem, since it is inefficient.

Resources

The 5th UESTC Programming Contest Final