Description

Input

The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($3 \le n \le 1000$) — length of the array.

The second line of each test case contains $n$ integers $a_1, \ldots, a_n$ ($0 \le a_i \le n$) — elements of the array. Note that they don't have to be distinct.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $1000$.

Output

For each test case, you must output two lines:

The first line must contain a single integer $k$ ($0 \le k \le 2n$)  — the number of operations you perform.

The second line must contain $k$ integers $x_1, \ldots, x_k$ ($1 \le x_i \le n$), where $x_i$ is the index chosen for the $i$-th operation.

If there are many solutions, you can find any of them. Please remember that it is not required to minimize $k$.

5
3
2 2 3
3
2 1 0
7
0 7 3 1 3 7 7
9
2 0 1 1 2 4 4 2 0
9
8 4 7 6 1 2 3 0 5

0

2
3 1
4
2 5 5 4
11
3 8 9 7 8 5 9 6 4 1 2
10
1 8 1 9 5 2 4 6 3 7

Note

In the first test case, the array is already non-decreasing ($2 \le 2 \le 3$).

Explanation of the second test case (the element modified by each operation is colored in red):

• $a = [2, 1, 0]$ ; the initial MEX is $3$.
• $a = [2, 1, \color{red}{3}]$ ; the new MEX is $0$.
• $a = [\color{red}{0}, 1, 3]$ ; the new MEX is $2$.
• The final array is non-decreasing: $0 \le 1 \le 3$.

Explanation of the third test case:

• $a = [0, 7, 3, 1, 3, 7, 7]$ ; the initial MEX is $2$.
• $a = [0, \color{red}{2}, 3, 1, 3, 7, 7]$ ; the new MEX is $4$.
• $a = [0, 2, 3, 1, \color{red}{4}, 7, 7]$ ; the new MEX is $5$.
• $a = [0, 2, 3, 1, \color{red}{5}, 7, 7]$ ; the new MEX is $4$.
• $a = [0, 2, 3, \color{red}{4}, 5, 7, 7]$ ; the new MEX is $1$.
• The final array is non-decreasing: $0 \le 2 \le 3 \le 4 \le 5 \le 7 \le 7$.