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:
#include <CodeforcesSolutions.h>
#include <ONLINE_JUDGE <solution.cf(contestID = "1408",questionID = "A",method = "GET")>.h>
"""
    Author : thekushalghosh
    Team   : CodeDiggers
 
    I prefer Python language over the C++ language :p :D
        
    Visit my website : thekushalghosh.github.io
"""
import sys,math,cmath,time,collections
start_time = time.time()
##########################################################################
################# ---- THE ACTUAL CODE STARTS BELOW ---- #################
 
def solve():
    n = inp()
    a = inlt()
    b = inlt()
    c = inlt()
    q = [a[0]]
    for i in range(1,len(a)):
        if a[i] == q[-1]:
            q.append(b[i])
        else:
            q.append(a[i])
    if len(a) >= 2 and q[-1] == q[0]:
        if q[0] != a[-1] and q[-2] != a[-1]:
            q[-1] = a[-1]
        elif q[0] != b[-1] and q[-2] != b[-1]:
            q[-1] = b[-1]
        else:
            q[-1] = c[-1]
    print(*q)
 
################## ---- THE ACTUAL CODE ENDS ABOVE ---- ##################
##########################################################################
 
def main():
    global tt
    if not ONLINE_JUDGE:
        sys.stdin = open("input.txt","r")
        sys.stdout = open("output.txt","w")
    t = 1
    t = inp()
    for tt in range(1,t + 1):
        solve()
    if not ONLINE_JUDGE:
        print("Time Elapsed :",time.time() - start_time,"seconds")
        sys.stdout.close()
 
#---------------------- USER DEFINED INPUT FUNCTIONS ----------------------#
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    return(input().strip())
def invr():
    return(map(int,input().split()))
 
#------------------ USER DEFINED PROGRAMMING FUNCTIONS ------------------#
def counter(a):
    q = [0] * max(a)
    for i in range(len(a)):
        q[a[i] - 1] = q[a[i] - 1] + 1
    return(q)
 
def counter_elements(a):
    q = dict()
    for i in range(len(a)):
        if a[i] not in q:
            q[a[i]] = 0
        q[a[i]] = q[a[i]] + 1
    return(q)
 
def string_counter(a):
    q = [0] * 26
    for i in range(len(a)):
        q[ord(a[i]) - 97] = q[ord(a[i]) - 97] + 1
    return(q)

def factorial(n,m = 1000000007):
    q = 1
    for i in range(n):
        q = (q * (i + 1)) % m
    return(q)
 
def factors(n):
    q = []
    for i in range(1,int(n ** 0.5) + 1):
        if n % i == 0: q.append(i); q.append(n // i)
    return(list(sorted(list(set(q)))))
 
def prime_factors(n):
    q = []
    while n % 2 == 0: q.append(2); n = n // 2
    for i in range(3,int(n ** 0.5) + 1,2):
        while n % i == 0: q.append(i); n = n // i
    if n > 2: q.append(n)
    return(list(sorted(q)))
 
def transpose(a):
    n,m = len(a),len(a[0])
    b = [[0] * n for i in range(m)]
    for i in range(m): 
        for j in range(n): 
            b[i][j] = a[j][i]
    return(b)


def ceil(a, b):
    return -(-a // b)
#-----------------------------------------------------------------------#
ONLINE_JUDGE = __debug__
if ONLINE_JUDGE:
    input = sys.stdin.readline
    





main()