A. Circle Coloring
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three sequences: $a_1, a_2, \ldots, a_n$; $b_1, b_2, \ldots, b_n$; $c_1, c_2, \ldots, c_n$.

For each $i$, $a_i \neq b_i$, $a_i \neq c_i$, $b_i \neq c_i$.

Find a sequence $p_1, p_2, \ldots, p_n$, that satisfy the following conditions:

• $p_i \in \{a_i, b_i, c_i\}$
• $p_i \neq p_{(i \mod n) + 1}$.

In other words, for each element, you need to choose one of the three possible values, such that no two adjacent elements (where we consider elements $i,i+1$ adjacent for $i<n$ and also elements $1$ and $n$) will have equal value.

It can be proved that in the given constraints solution always exists. You don't need to minimize/maximize anything, you need to find any proper sequence.

Input

The first line of input contains one integer $t$ ($1 \leq t \leq 100$): the number of test cases.

The first line of each test case contains one integer $n$ ($3 \leq n \leq 100$): the number of elements in the given sequences.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 100$).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \leq b_i \leq 100$).

The fourth line contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \leq c_i \leq 100$).

It is guaranteed that $a_i \neq b_i$, $a_i \neq c_i$, $b_i \neq c_i$ for all $i$.

Output

For each test case, print $n$ integers: $p_1, p_2, \ldots, p_n$ ($p_i \in \{a_i, b_i, c_i\}$, $p_i \neq p_{i \mod n + 1}$).

If there are several solutions, you can print any.

Example
Input
5
3
1 1 1
2 2 2
3 3 3
4
1 2 1 2
2 1 2 1
3 4 3 4
7
1 3 3 1 1 1 1
2 4 4 3 2 2 4
4 2 2 2 4 4 2
3
1 2 1
2 3 3
3 1 2
10
1 1 1 2 2 2 3 3 3 1
2 2 2 3 3 3 1 1 1 2
3 3 3 1 1 1 2 2 2 3

Output
1 2 3
1 2 1 2
1 3 4 3 2 4 2
1 3 2
1 2 3 1 2 3 1 2 3 2

Note

In the first test case $p = [1, 2, 3]$.

It is a correct answer, because:

• $p_1 = 1 = a_1$, $p_2 = 2 = b_2$, $p_3 = 3 = c_3$
• $p_1 \neq p_2$, $p_2 \neq p_3$, $p_3 \neq p_1$

All possible correct answers to this test case are: $[1, 2, 3]$, $[1, 3, 2]$, $[2, 1, 3]$, $[2, 3, 1]$, $[3, 1, 2]$, $[3, 2, 1]$.

In the second test case $p = [1, 2, 1, 2]$.

In this sequence $p_1 = a_1$, $p_2 = a_2$, $p_3 = a_3$, $p_4 = a_4$. Also we can see, that no two adjacent elements of the sequence are equal.

In the third test case $p = [1, 3, 4, 3, 2, 4, 2]$.

In this sequence $p_1 = a_1$, $p_2 = a_2$, $p_3 = b_3$, $p_4 = b_4$, $p_5 = b_5$, $p_6 = c_6$, $p_7 = c_7$. Also we can see, that no two adjacent elements of the sequence are equal.