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.

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
 
 
 
 
 
 
 
 
 
 

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.