Problem: You are given three sequences: a_1, a_2, …, a_n; b_1, b_2, …, b_n; c_1, c_2, …, c_n.

For each i, a_i ≠ b_i, a_i ≠ c_i, b_i ≠ c_i.

Find a sequence p_1, p_2, …, p_n, that satisfy the following conditions:

  * p_i ∈ \\{a_i, b_i, c_i\}
  * p_i ≠ 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 ≤ t ≤ 100): the number of test cases.

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

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 100).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 100).

The fourth line contains n integers c_1, c_2, …, c_n (1 ≤ c_i ≤ 100).

It is guaranteed that a_i ≠ b_i, a_i ≠ c_i, b_i ≠ c_i for all i.

Output

For each test case, print n integers: p_1, p_2, …, p_n (p_i ∈ \\{a_i, b_i, c_i\}, p_i ≠ 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 ≠ p_2 , p_2 ≠ p_3 , p_3 ≠ 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.

Solution (in PYTHON3):

Solution:
def parser():
    while 1:
        data = list(input().split(' '))
        for number in data:
            if len(number) > 0:
                yield(number)

input_parser = parser()

def get_word():
    global input_parser
    return next(input_parser)

def get_number():
    data = get_word()
    try:
        return int(data)
    except ValueError:
        return float(data)

def generate_word(n, long_word):
    target = ''
    counter = 0
    while(n != 0):
        target = target + long_word[counter]
        long_word = long_word[1:]
        n = n-1
        counter = counter + 1
    print(target)



test_cases = get_number()
for i in range(0, test_cases):
    n = get_number()
    a = []
    b = []
    c = []
    final = []
    for i in range(n):
        a.append(get_number())
    for i in range(n):
        b.append(get_number())
    for i in range(n):
        c.append(get_number())
    
    final.append(a[0])
    for i in range(0, n - 1):
        my_next = i + 1
        if(my_next == n - 1):
            if(final[i] != a[my_next] and a[my_next] != final[0]):
                final.append(a[my_next])
                continue
            if(final[i] != b[my_next] and b[my_next] != final[0]):
                final.append(b[my_next])
                continue
            if(final[i] != c[my_next] and c[my_next] != final[0]):
                final.append(c[my_next])
                continue
        else:
            if(final[i] != a[my_next]):
                final.append(a[my_next])
                continue
            if(final[i] != b[my_next]):
                final.append(b[my_next])
                continue
            if(final[i] != c[my_next]):
                final.append(c[my_next])
                continue

    print (' '.join(str(i) for i in final))