Problem Statement

You are given binary strings $A = A_1 A_2 \ldots A_N$ and $B = B_1 B_2 \ldots B_N$ of length $N$.

You can perform $M$ types of operations. The $i$-th type of operation is represented by a pair of integers $(x_i, y_i)$ with $1 \le x_i, y_i \le N$, and it flips the value of $A_{y_i}$ when $A_{x_i} = 1$. It is possible that $x_i = y_i$. Here, flipping means changing $0$ to $1$ or $1$ to $0$.

Determine whether it is possible to convert $A$ into a string equal to $B$ by performing at most $2N$ operations on $A$, and if so, construct one such way.

You are given $T$ test cases; solve each one.

Constraints

• $1 \le T \le 2 \times 10^5$
• $1 \le N \le 2 \times 10^5$
• $1 \le M \le 2 \times 10^5$
• $A$ and $B$ are binary strings of length $N$.
• $A \neq B$
• $1 \le x_i \le N$ ($1 \le i \le M$)
• $1 \le y_i \le N$ ($1 \le i \le M$)
• The sum of $N$ and $M$ over all test cases is at most $2 \times 10^5$.
• $T$, $N$, $M$, $x_i$, $y_i$ are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N
A
B
M
x_1 y_1
x_2 y_2
\vdots
x_M y_M

Output

Output for the $T$ test cases in order.

For each test case, output as follows.

If no sequence of operations satisfying the condition exists, output -1 on a single line.

If a sequence of operations satisfying the condition exists, let $K$ be the length of the sequence of operations and $C_i$ be the index of the $i$-th operation performed, and output as follows:

K
C_1 C_2 \ldots C_K

Here, $K$ must be at most $2N$, and operation $i$ must not be performed when $A_{x_i} = 0$.