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:
from bisect import *
from collections import *
from math import *
from heapq import *
from typing import List
from itertools import *
from operator import *
from functools import *
import sys
'''
@lru_cache(None)
def fact(x):
    if x<2:
        return 1
    return fact(x-1)*x

@lru_cache(None)
def per(i,j):
    return fact(i)//fact(i-j)

@lru_cache(None)
def com(i,j):
    return per(i,j)//fact(j)

def linc(f,t,l,r):
    while l<r:
        mid=(l+r)//2
        if t>f(mid):
            l=mid+1
        else:
            r=mid
    return l

def rinc(f,t,l,r):
    while l<r:
        mid=(l+r+1)//2
        if t<f(mid):
            r=mid-1
        else:
            l=mid
    return l

def ldec(f,t,l,r):
    while l<r:
        mid=(l+r)//2
        if t<f(mid):
            l=mid+1
        else:
            r=mid
    return l

def rdec(f,t,l,r):
    while l<r:
        mid=(l+r+1)//2
        if t>f(mid):
            r=mid-1
        else:
            l=mid
    return l

def isprime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
    return True

def power2(n):
    while not n&1:
        n>>=1
    return n==1
'''
'''
import time
s=time.time()
e=time.time()
print(e-s)
'''

t=int(input())
for i in range(t):
    #n,m=map(int,input().split())
    n=int(input())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))
    c=list(map(int,input().split()))
    ans=[a[0]]
    for i in range(1,n-1):
        if ans[-1]!=a[i]:
            tmp=a[i]
        else:
            tmp=b[i]
        ans.append(tmp)
    if a[-1]!=ans[0] and a[-1]!=ans[-1]:
        ans.append(a[-1])
    elif b[-1]!=ans[0] and b[-1]!=ans[-1]:
        ans.append(b[-1])
    else:
        ans.append(c[-1])
    print(*ans)
'''
n,m=map(int,input().split())
graph=defaultdict(dict)
for i in range(m):
    u,v,w=map(int,input().split())
    graph[u][v]=w
    graph[v][u]=w
def dij(u,v):
    graph[u][v]*=2
    graph[v][u]*=2
    d={}
    d[1]=0
    for i in range(2,n+1):
        d[i]=inf
    remain=set(range(2,n+1))
    for i in graph[1]:
        d[i]=graph[1][i]
    while remain:
        k=min(remain,key=lambda x: d[x])
        remain.remove(k)
        for i in remain:
            if i in graph[k]:
                d[i]=min(d[i],d[k]+graph[k][i])
    graph[u][v]//=2
    graph[v][u]//=2
    return d[n]
D={}
D[1]=0
for i in range(2,n+1):
    D[i]=inf
remain=set(range(2,n+1))
pre=[-1]*(n+1)
for i in graph[1]:
    D[i]=graph[1][i]
    pre[i]=1
while remain:
    k=min(remain,key=lambda x: D[x])
    remain.remove(k)
    for i in remain:
        if i in graph[k]:
            if D[i]>D[k]+graph[k][i]:
                D[i]=D[k]+graph[k][i]
                pre[i]=k
cur=ans=D[n]
node=n
while pre[node]!=-1:
    ans=max(ans,dij(node,pre[node]))
    node=pre[node]
print(ans-cur)
            
'''