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>
const int md = 998244353;
using namespace std;
using namespace std::chrono;
long long pw(long long a, long long b) {
  long long c = 1, m = a;
  while (b) {
    if (b & 1) c = (c * m);
    m = (m * m);
    b /= 2;
  }
  return c;
}
long long pwmd(long long a, long long b) {
  long long c = 1, m = a;
  while (b) {
    if (b & 1) c = (c * m) % md;
    m = (m * m) % md;
    b /= 2;
  }
  return c;
}
long long modinv(long long n) { return pwmd(n, md - 2); }
long long inverse(long long i) {
  if (i == 1) return 1;
  return (md - ((md / i) * inverse(md % i)) % md + md) % md;
}
int ceel(int a, int b) {
  if (a % b == 0)
    return a / b;
  else
    return a / b + 1;
}
long long my_log(long long n, long long b) {
  long long i = 1;
  long long ans = 0;
  while (1) {
    if (i > n) {
      ans--;
      break;
    }
    if (i == n) break;
    i *= b;
    ans++;
  }
  return ans;
}
bool sortbysec(const pair<long long, long long> &a,
               const pair<long long, long long> &b) {
  return (a.second < b.second);
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
vector<char> capl = {'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I',
                     'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R',
                     'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'};
vector<char> sml = {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i',
                    'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r',
                    's', 't', 'u', 'v', 'w', 'x', 'y', 'z'};
string conv(long long a) {
  string b;
  long long e = 2;
  long long c = my_log(a, e);
  c++;
  b = '1';
  for (int i = 0; i < c - 1; i++) {
    long long k = a >> (c - 2 - i);
    if (k & 1)
      b += '1';
    else
      b += '0';
  }
  if (a == 0) return "0";
  return b;
}
long long mysqt(long long a) {
  long long ans = 1;
  while (ans * ans <= a) ans++;
  ans--;
  return ans;
}
bool isprime(int p) {
  int i = 2;
  while (i <= sqrt(p)) {
    if (p % i == 0) {
      return false;
    }
    i++;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int t, n, a, b, c;
  cin >> t;
  while (t--) {
    cin >> n;
    vector<int> v1, v2, v3;
    for (int i = 0; i < n; i++) cin >> a, v1.push_back(a);
    for (int i = 0; i < n; i++) cin >> a, v2.push_back(a);
    for (int i = 0; i < n; i++) cin >> a, v3.push_back(a);
    vector<int> ans;
    ans.push_back(v1[0]);
    for (int i = 1; i < n; i++) {
      if (i < n - 1) {
        if (v1[i] != ans[i - 1])
          ans.push_back(v1[i]);
        else if (v2[i] != ans[i - 1])
          ans.push_back(v2[i]);
        else
          ans.push_back(v3[i]);
      } else {
        if (v1[i] != ans[i - 1] && v1[i] != ans[0])
          ans.push_back(v1[i]);
        else if (v2[i] != ans[i - 1] && v2[i] != ans[0])
          ans.push_back(v2[i]);
        else
          ans.push_back(v3[i]);
      }
    }
    for (auto x : ans) cout << x << " ";
    cout << "\n";
  }
}