Problem Statement

You are given a positive integer $N$, and length-$N$ integer sequences, $X=(X_1,X_2,\dots ,X_N)$ and $Y=(Y_1,Y_2,\dots ,Y_N)$.

Additionally, you are given length-$N$ integer sequences, $A=(A_1,A_2,\dots ,A_N)$ and $B=(B_1,B_2,\dots ,B_N)$.

Determine whether it is possible to make $A$ match $B$ by performing the following operations any number of times between $0$ and $2N$ (inclusive) in total, and if it is possible, output one such procedure.

• chmax: Choose integers $l$ and $r$ such that $1\le l\le r\le N$. For $i=l,l+1,\dots ,r$, replace $A_i$ with $\max(A_i,X_{r-l+1})$.
• chmin: Choose integers $l$ and $r$ such that $1\le l\le r\le N$. For $i=l,l+1,\dots ,r$, replace $A_i$ with $\min(A_i,Y_{r-l+1})$.

You are given $T$ test cases; solve each of them.

Constraints

• $1 \le T \le 10^5$
• $1 \le N \le 400$
• $1 \le X_i,Y_i,A_i,B_i\le N$
• The sum of $N^3$ over all test cases is at most $400^3$.
• All input values are integers.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{test}_i$ denotes the $i$-th test case.

T
\mathrm{test}_1
\mathrm{test}_2
\vdots
\mathrm{test}_T

Each test case is given in the following format:

N
X_1 X_2 \dots X_N
Y_1 Y_2 \dots Y_N
A_1 A_2 \dots A_N
B_1 B_2 \dots B_N

Output

For each of the $T$ test cases, in order, output as follows.

If it is impossible to make $A$ match $B$, output -1.

If it is possible, letting $K\ (0\le K\le 2N)$ be the number of operations performed, output in the following format:

K
\mathrm{op}_1 l_1 r_1
\mathrm{op}_2 l_2 r_2
\vdots
\mathrm{op}_K l_K r_K

Here, $\mathrm{op}_i$, $l_i$, and $r_i$ represent the $i$-th operation. $\mathrm{op}_i$ is chmax or chmin, representing the type of the $i$-th operation. $l_i$ and $r_i$ are the $l$ and $r$ chosen in the $i$-th operation, respectively.