CF1789D.Serval and Shift-Shift-Shift

Serval has two $n$ -bit binary integer numbers $a$ and $b$ . He wants to share those numbers with Toxel.

Since Toxel likes the number $b$ more, Serval decides to change $a$ into $b$ by some (possibly zero) operations. In an operation, Serval can choose any positive integer $k$ between $1$ and $n$ , and change $a$ into one of the following number:

• $a\oplus(a\ll k)$
• $a\oplus(a\gg k)$

In other words, the operation moves every bit of $a$ left or right by $k$ positions, where the overflowed bits are removed, and the missing bits are padded with $0$ . The bitwise XOR of the shift result and the original $a$ is assigned back to $a$ .

Serval does not have much time. He wants to perform no more than $n$ operations to change $a$ into $b$ . Please help him to find out an operation sequence, or determine that it is impossible to change $a$ into $b$ in at most $n$ operations. You do not need to minimize the number of operations.

In this problem, $x\oplus y$ denotes the bitwise XOR operation of $x$ and $y$ . $a\ll k$ and $a\gg k$ denote the logical left shift and logical right shift.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1\le t\le2\cdot10^{3}$ ). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1\le n\le2\cdot10^{3}$ ) — the number of bits in numbers $a$ and $b$ .

The second and the third line of each test case contain a binary string of length $n$ , representing $a$ and $b$ , respectively. The strings contain only characters 0 and 1.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot10^{3}$ .

For each test case, if it is impossible to change $a$ into $b$ in at most $n$ operations, print a single integer $-1$ .

Otherwise, in the first line, print the number of operations $m$ ( $0\le m\le n$ ).

If $m>0$ , in the second line, print $m$ integers $k_{1},k_{2},\dots,k_{m}$ representing the operations. If $1\le k_{i}\le n$ , it means logical left shift $a$ by $k_{i}$ positions. If $-n\le k_{i}\le-1$ , it means logical right shift $a$ by $-k_{i}$ positions.

If there are multiple solutions, print any of them.

In the first test case:

The first operation changes $a$ into $00111\oplus\sout{001}11\underline{000}=11111$ .

The second operation changes $a$ into $11111\oplus\underline{00}111\sout{11}=11000$ .

The bits with strikethroughs are overflowed bits that are removed. The bits with underline are padded bits.

In the second test case, $a$ is already equal to $b$ , so no operations are needed.

In the third test case, it can be shown that $a$ cannot be changed into $b$ .