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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<bool> prime(200002, true);
void seive(long long mx) {
  prime[0] = prime[1] = false;
  for (long long i = 2; i * i <= mx; i++) {
    if (prime[i]) {
      for (long long j = i * i; j <= mx; j += i) {
        prime[j] = false;
      }
    }
  }
}
const long long M = 1e9 + 7;
const long long Mxn = 3e5;
long long power(long long i, long long p) {
  long long ans = 1;
  while (p) {
    if (p & 1) ans = (ans * i) % M;
    i = (i * i) % M;
    p /= 2;
  }
  return ans % M;
}
int main() {
  int t = 1;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    vector<vector<long long>> v(n, vector<long long>(3, 0));
    vector<long long> ans(n);
    for (long long j = 0; j < 3; j++) {
      for (long long i = 0; i < n; i++) {
        cin >> v[i][j];
      }
    }
    for (long long i = 0; i < n; i++) sort(v[i].begin(), v[i].end());
    ans[0] = v[0][0];
    for (long long i = 1; i < n - 1; i++) {
      long long k = 0;
      while (ans[i - 1] == v[i][k]) {
        k++;
        k %= 3;
      }
      ans[i] = v[i][k];
    }
    long long k = 0;
    while (v[n - 1][k] == ans[n - 2] || v[n - 1][k] == ans[0]) {
      k++;
      k %= 3;
    }
    ans[n - 1] = v[n - 1][k];
    for (auto x : ans) cout << x << " ";
    cout << endl;
  }
  return 0;
}