Equalize by Divide

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. Descriptions of test cases follow.

The first line of each test case description contains a single integer $$$n$$$ ($$$1 \leq n \leq 100$$$).

The second line of each test case description contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$).

It is guaranteed, that the sum of $$$n$$$ for all test cases does not exceed $$$1000$$$.

Output:

For each test case print a single integer $$$q$$$ ($$$-1 \leq q \leq 30n$$$). If $$$q=-1$$$, there is no solution, otherwise $$$q$$$ is equal to the number of operations.

If $$$q \geq 0$$$, on the next $$$q$$$ lines print two integers $$$i$$$, $$$j$$$ ($$$1 \leq i, j \leq n$$$, $$$i \neq j$$$) — descriptions of operations.

If there are multiple solutions, you can print any.

Sample Input:

10
1
100
3
1 1 1
2
2 1
2
5 5
3
4 3 2
4
3 3 4 4
2
2 100
5
5 3 6 7 8
6
3 3 80 3 8 3
4
19 40 19 55

Sample Output:

0
0
-1
0
2
1 3
2 1
4
3 1
4 2
1 3
2 4
6
2 1
2 1
2 1
2 1
2 1
2 1
8
5 2
4 2
3 2
1 3
1 3
2 1
4 1
5 1
4
5 1
3 1
3 1
3 1
9
4 2
2 1
1 2
1 2
3 2
3 2
1 4
2 4
3 4

Note:

In the first and second, fourth test cases all numbers are equal, so it is possible to do nothing.

In the third test case, it is impossible to make all numbers equal.

In the fifth test case: $$$[\color{red}{4}, 3, \color{blue}{2}] \to [\color{blue}{2}, \color{red}{3}, 2] \to [2, 2, 2]$$$.

In the sixth test case: $$$[\color{blue}{3}, 3, \color{red}{4}, 4] \to [3, \color{blue}{3}, 2, \color{red}{4}] \to [\color{red}{3}, 3, \color{blue}{2}, 2] \to [2, \color{red}{3}, 2, \color{blue}{2}] \to [2, 2, 2, 2]$$$.

Here the red numbers are $$$i$$$ indices (that will be assigned), blue numbers are $$$j$$$ indices.