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 ll = long long;
using pii = std::pair<int, int>;
using vi = std::vector<int>;
using vii = std::vector<pii>;
using std::cin;
using std::cout;
using std::sort;
using std::string;
using std::vector;
const int inf = 0x3f3f3f3f;
const int MOD = 1000000007;
int powm(int x, int n) {
  int r = 1;
  while (n) {
    if (n & 1) r = (r * 1LL * x) % MOD;
    x = (x * 1LL * x) % MOD;
    n /= 2;
  }
  return r;
}
int inv(int x) { return powm(x, MOD - 2); }
int a[3][128];
void solve() {
  int n;
  cin >> n;
  for (int j = 0, nnnn = (3); j < nnnn; ++j) {
    for (int i = 0, nnnn = (n); i < nnnn; ++i) cin >> a[j][i];
    a[j][n] = a[j][0];
  }
  vi p(n + 1);
  p[0] = a[0][0];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    for (int j = 0, nnnn = (3); j < nnnn; ++j)
      if (p[i] != a[j][i + 1]) p[i + 1] = a[j][i + 1];
  }
  for (int j = 0, nnnn = (3); j < nnnn; ++j)
    if (a[j][n - 1] != p[0] && (n < 2 || a[j][n - 1] != p[n - 2]))
      p[n - 1] = a[j][n - 1];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) cout << p[i] << ' ';
  cout << '\n';
}
int main(int argc, char* argv[]) {
  ::std::ios::sync_with_stdio(false);
  ::std::cin.tie(0);
  ::std::cout.tie(0);
  int tc = 1;
  std::cin >> tc;
  while (tc--) solve();
  return 0;
}