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 sys
# import math
# import bisect
# import collections
# import itertools
# #from sys import stdin,stdout
# from math import gcd,floor,sqrt,log
# from collections import defaultdict as dd, Counter as ctr
# from bisect import bisect_left as bl, bisect_right as br
# from itertools import permutations as pr, combinations as cb

#sys.setrecursionlimit(100000000)

#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$

inp    = lambda: int(input())
# strng  = lambda: input().strip()
# jn     = lambda  x,l: x.join(map(str,l))
# strl   = lambda: list(input().strip())
# mul    = lambda: map(int,input().strip().split())
# mulf   = lambda: map(float,input().strip().split())
seq    = lambda: list(map(int,input().strip().split()))

#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$
# p_inf = float('inf')
# n_inf = float('-inf')
#To find mex 
# def mex(arr):
#     nList = set(arr)
#     mex = 0
#     while mex in nList:
#         mex += 1
#     return(mex)

def results(a, b, c, n):
    temp = [a[0]]
    for i in range(1, n - 1):
        if(a[i] != temp[i - 1]):
            temp.append(a[i])
        elif(b[i] != temp[i - 1]):
            temp.append(b[i])
        else:
            temp.append(c[i])
    if(a[n - 1] != temp[0] and a[n - 1] != temp[-1]):
        temp.append(a[n - 1])
    elif(b[n - 1] != temp[0] and b[n - 1] != temp[-1]):
        temp.append(b[n - 1])
    else:
        temp.append(c[n - 1])
    return(temp)

def main():
    t = inp()
    for _ in range(t):
        n = inp()
        a = seq()
        b = seq()
        c = seq()
        result = results(a,b,c,n)
        print(*result)

if __name__ == '__main__':
    main()