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 = 1005;
int a[maxn][4];
bool dp[maxn][4];
int fa[maxn][4];
int stk[maxn], tot = 0;
int main() {
  int T;
  cin >> T;
  while (T--) {
    int n;
    scanf("%d", &n);
    for (int k = 0; k < 3; ++k) {
      for (int i = 0; i < n; ++i) {
        scanf("%d", &a[i][k]);
      }
    }
    for (int k = 0; k < 3; ++k) {
      a[n][k] = a[0][k];
    }
    bool flag = false;
    for (int kk = 0; kk < 3 && !flag; ++kk) {
      memset(dp, 0, sizeof(dp));
      memset(fa, 0, sizeof(fa));
      dp[0][kk] = true;
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < 3; ++j) {
          if (!dp[i][j]) continue;
          for (int k = 0; k < 3; ++k) {
            if (a[i][j] != a[i + 1][k]) {
              dp[i + 1][k] = true;
              fa[i + 1][k] = j;
            }
          }
        }
      }
      if (dp[n][kk]) {
        tot = 0;
        for (int i = n, j = kk; i > 0; i--) {
          j = fa[i][j];
          stk[tot++] = a[i - 1][j];
        }
        while (tot) {
          if (tot > 1)
            printf("%d ", stk[tot - 1]);
          else
            printf("%d\n", stk[tot - 1]);
          tot--;
        }
        break;
      }
    }
  }
}