Description

Arahc has a sequence $a_n$ of size $n\,(1\leq n\leq 10^5)$. He wants you to sort it in ascending order.

You can perform at most $3 \times 10^5$ operations. In each operation, you select an index $i$, and reverse the substrings $a_{1 \ldots i-1}$ and $a_{i+1 \ldots n}$ (If exists). For example, if the sequence is $1, 4, 3, 5, 3, 2$ and you select $i = 4$, the sequence will become $3, 4, 1, 5, 2, 3$.

If no solution within $3 \times 10^5$ operations exists, output $-1$.

Format

Input

The first line contains a single integer $T\,(1\leq T\leq 5)$, the number of test cases. For each test case:

The first line contains a single integer $n\,(1\leq n\leq 10^5)$, the size of the sequence.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n\,(1\leq a_i\leq n)$.

Output

For each test case:

If no solution within $3 \times 10^5$ operations exists, output $-1$.

Otherwise, the first line contains a single integer $k\,(1\leq k\leq 3 \times 10^5)$, the number of operations you will perform.

The next line contains $k$ integers $i_1, i_2, \ldots, i_k\,(1\leq i_j\leq n)$, where $i_j$ is the index you select in the $j$-th operation.

Samples

2
6
1 4 3 5 3 2
2
2 1

5
5 3 6 2 4
-1