Bubble Gum Sort

Ecrade_ has an integer sequence of length $$$n$$$, denoted as $$$a_1, a_2, \ldots, a_n$$$.

You can perform several operations on this sequence. In each operation, you can choose an index $$$p\ (1\le p \lt n)$$$, increment $$$a_{p+1}$$$ by $$$1$$$, and then swap $$$a_p$$$ and $$$a_{p+1}$$$.

Ecrade_ wants you to transform the sequence into a strictly increasing sequence within $$$n^2-n$$$ operations, or report that it is impossible to achieve this goal.

Input

The first line contains an integer $$$T\ (1\le T\le 10)$$$, representing the number of test cases.

For each test case:

The first line contains an integer $$$n\ (2\le n,\sum n\le 500)$$$.
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n\ (1\le a_i\le 10^9)$$$.

Output

For each test case:

If it is possible to transform the sequence $$$a$$$ into a strictly increasing sequence within $$$n^2-n$$$ operations:
- First, output a line with an integer $$$k\ (0\le k\le n^2-n)$$$, indicating the number of operations.
- Then, output a line with $$$k$$$ integers $$$p_1, p_2, \ldots, p_k\ (1\le p_i \lt n)$$$, indicating the indices chosen in each operation.
- If there are multiple valid sequences of operations, output any one of them.
Otherwise, output a line with -1.

Example

Input

Output

Note

For the first test case, the sequence $$$[1,2]$$$ is already a strictly increasing sequence.
For the second test case, it is impossible to transform the sequence $$$[2,1]$$$ into a strictly increasing sequence within the allowed number of operations.
For the third test case, first choose index $$$2$$$, transforming the sequence to $$$[4,2,5]$$$; then choose index $$$1$$$, transforming the sequence to $$$[3,4,5]$$$.