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:
import os
import math

true = True;
false = False;

# from collections import defaultdict, deque
from functools import reduce

is_dev = 'vscode' in os.environ

if is_dev:
    inF = open('in.txt', 'r')
    outF = open('out.txt', 'w')

def ins():
    return list(map(int, input_().split(' ')))

def inss():
    return list(input_().split(' '))

def input_():
    if is_dev:
        return inF.readline()[:-1]
    else:
        return input()
    
def ranin():
    return range(int(input_()))

def print_(data):
    if is_dev:
        outF.write(str(data)+'\n')
    else:
        print(data)

for _ in range(int(input_())):
    n = int(input_())
    
    a = ins()
    b = ins()
    c = ins()
    
#     a.append(a[0])
#     b.append(b[0])
#     c.append(c[0])
    
    result = [a[-1]]
    for i in range(n-1):
        ai = a[i]
        bi = b[i]
        ci = c[i]
        
        if ai != result[-1]:
            result.append(ai)
        elif bi != result[-1]:
            result.append(bi)
        elif ci != result[-1]:
            result.append(ci)
        else:
            raise Exception('Wrong answer')
    result.pop(0)
    ai = a[-1]
    bi = b[-1]
    ci = c[-1]
    if ai != result[0] and ai != result[-1]:
        result.append(ai)
    elif bi != result[0] and bi != result[-1]:
        result.append(bi)
    elif ci != result[0] and ci != result[-1]:
        result.append(ci)
    else:
        raise Exception('Wrong answer')
        
    print_(' '.join(map(str, result)))
    
        
    
if is_dev:
    outF.close()
    def compare_file():
        print(open('out.txt', 'r').read() == open('outactual.txt', 'r').read())
    compare_file()