Description

The ACM Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 gcd(a,b) = 1 arranged in increasing order. The first few are

F2 = {1/2}

F3 = {1/3, 1/2, 2/3}

F4 = {1/4, 1/3, 1/2, 2/3, 3/4}

F5 = {1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5}

Now, your task is to print ACM 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<=n<=3000).

Output

For each test case, you should output one line, which contains the corresponding ACM 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.

Sample

Input

4
2
3
4
5

Output

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

Source: lily