Problem: We guessed a permutation p consisting of n integers. The permutation of length n is the array of length n where each element from 1 to n appears exactly once. This permutation is a secret for you.

For each position r from 2 to n we chose some other index l (l < r) and gave you the segment p_l, p_{l + 1}, ..., p_r in sorted order (i.e. we rearranged the elements of this segment in a way that the elements of this segment are sorted). Thus, you are given exactly n-1 segments of the initial permutation but elements inside each segment are sorted. The segments are given to you in random order.

For example, if the secret permutation is p=[3, 1, 4, 6, 2, 5] then the possible given set of segments can be:

  * [2, 5, 6] 
  * [4, 6] 
  * [1, 3, 4] 
  * [1, 3] 
  * [1, 2, 4, 6] 



Your task is to find any suitable permutation (i.e. any permutation corresponding to the given input data). It is guaranteed that the input data corresponds to some permutation (i.e. such permutation exists).

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (2 ≤ n ≤ 200) — the length of the permutation.

The next n-1 lines describe given segments.

The i-th line contains the description of the i-th segment. The line starts with the integer k_i (2 ≤ k_i ≤ n) — the length of the i-th segment. Then k_i integers follow. All integers in a line are distinct, sorted in ascending order, between 1 and n, inclusive.

It is guaranteed that the required p exists for each test case.

It is also guaranteed that the sum of n over all test cases does not exceed 200 (∑ n ≤ 200).

Output

For each test case, print the answer: n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, all p_i should be distinct) — any suitable permutation (i.e. any permutation corresponding to the test case input).

Example

Input


5
6
3 2 5 6
2 4 6
3 1 3 4
2 1 3
4 1 2 4 6
5
2 2 3
2 1 2
2 1 4
2 4 5
7
3 1 2 6
4 1 3 5 6
2 1 2
3 4 5 7
6 1 2 3 4 5 6
3 1 3 6
2
2 1 2
5
2 2 5
3 2 3 5
4 2 3 4 5
5 1 2 3 4 5


Output


3 1 4 6 2 5 
3 2 1 4 5 
2 1 6 3 5 4 7 
1 2 
2 5 3 4 1 

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class CFA {
  BufferedReader br;
  PrintWriter out;
  StringTokenizer st;
  boolean eof;
  private static final long MOD = 1000L * 1000L * 1000L + 7;
  private static final int[] dx = {0, -1, 0, 1};
  private static final int[] dy = {1, 0, -1, 0};
  private static final String yes = "Yes";
  private static final String no = "No";

  void solve() {
    int T = nextInt();
//    int T = 1;
    for (int i = 0; i < T; i++) {
      helper();
    }
  }

  List<Set<Integer>> all;
  int n;
  void helper() {
    n = nextInt();
    all = new ArrayList<>();
    for (int i = 0; i < n - 1; i++) {
      int cnt = nextInt();
      Set<Integer> ind = new HashSet<>();
      for (int j = 0; j < cnt; j++) {
        int val = nextInt() - 1;
        ind.add(val);
      }
      all.add(ind);
    }

    for (int i = 0; i < n; i++) {
      int[] res = new int[n];
      res[0] = i;

      List<Set<Integer>> tmp = new ArrayList<>();
      for (Set<Integer> ls : all) {
        tmp.add(new HashSet<>(ls));
      }
      boolean valid = true;
      for (int j = 1; j < n; j++) {
        List<Set<Integer>> nxt = new ArrayList<>();
        Set<Integer> one = null;
        int cntOne = 0;
        for (Set<Integer> ls : tmp) {
          ls.remove(res[j - 1]);
          if (ls.size() == 1) {
            one = ls;
            cntOne++;
          } else if (!ls.isEmpty()) {
            nxt.add(ls);
          }
        }

        if (cntOne != 1) {
          valid = false;
          break;
        }

        int single = -1;
        for (int v : one) {
          single = v;
        }

        res[j] = single;
        tmp = nxt;
      }

      if (!valid) {
        continue;
      }
      if (isValid(res)) {
        for (int v : res) {
          out((v + 1) + " ");
        }
        outln("");
        return;
      }
    }
    throw new RuntimeException("Should not happend!!!");
  }

  boolean isValid(int[] res) {
    int[] map = new int[n];
    for (int i = 0; i < n; i++) {
      map[res[i]] = i;
    }
    for (Set<Integer> ls : all) {
      int min = Integer.MAX_VALUE;
      int max = Integer.MIN_VALUE;
      for (int v : ls) {
        min = Math.min(min, map[v]);
        max = Math.max(max, map[v]);
      }
      if (max - min + 1 != ls.size()) {
        return false;
      }
    }
    return true;
  }

  void shuffle(long[] a) {
    int n = a.length;
    for(int i = 0; i < n; i++) {
      int r = i + (int) (Math.random() * (n - i));
      long tmp = a[i];
      a[i] = a[r];
      a[r] = tmp;
    }
  }

  long gcd(long a, long b) {
    while(a != 0 && b != 0) {
      long c = b;
      b = a % b;
      a = c;
    }
    return a + b;
  }
  private void outln(Object o) {
    out.println(o);
  }
  private void out(Object o) {
    out.print(o);
  }
  private void formatPrint(double val) {
    outln(String.format("%.9f%n", val));
  }
  public CFA() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);
    solve();
    out.close();
  }
  public static void main(String[] args) {
    new CFA();
  }

  public long[] nextLongArr(int n) {
    long[] res = new long[n];
    for(int i = 0; i < n; i++)
      res[i] = nextLong();
    return res;
  }
  public int[] nextIntArr(int n) {
    int[] res = new int[n];
    for(int i = 0; i < n; i++)
      res[i] = nextInt();
    return res;
  }
  public String nextToken() {
    while (st == null || !st.hasMoreTokens()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (Exception e) {
        eof = true;
        return null;
      }
    }
    return st.nextToken();
  }
  public String nextString() {
    try {
      return br.readLine();
    } catch (IOException e) {
      eof = true;
      return null;
    }
  }
  public int nextInt() {
    return Integer.parseInt(nextToken());
  }
  public long nextLong() {
    return Long.parseLong(nextToken());
  }
  public double nextDouble() {
    return Double.parseDouble(nextToken());
  }
}