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;
const int MAXN = 5e3 + 11;
const int INF = 0x3f3f3f3f;
const int MOD = 998244353;
int T, n;
int w[111][3], dp[111][3];
void print(int i, int u) {
  if (i == -1) return;
  print(i - 1, dp[i][u]);
  printf("%d%c", w[i][u], i == n - 1 ? '\n' : ' ');
}
int main() {
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &n);
    for (int(i) = (0); (i) < (3); (i)++)
      for (int(j) = (0); (j) < (n); (j)++) scanf("%d", &w[j][i]);
    for (int(t) = (0); (t) < (3); (t)++) {
      for (int(i) = (0); (i) < (3); (i)++)
        for (int(j) = (0); (j) < (n); (j)++) dp[j][i] = -1;
      dp[0][t] = 0;
      for (int(i) = (1); (i) < (n); (i)++)
        for (int(j) = (0); (j) < (3); (j)++) {
          for (int(k) = (0); (k) < (3); (k)++)
            if (w[i][j] != w[i - 1][k] && dp[i - 1][k] != -1) {
              dp[i][j] = k;
              break;
            }
        }
      bool pd;
      pd = 0;
      for (int(i) = (0); (i) < (3); (i)++)
        if (w[n - 1][i] != w[0][t] && dp[n - 1][i] != -1) {
          pd = 1;
          print(n - 1, i);
          break;
        }
      if (pd) break;
    }
  }
  return 0;
}