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A. Circle Coloring

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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