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.io.*;
import java.util.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Housni Abdellatif
 */
public class Main {
    public static void main(String[] args) throws IOException{
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        TaskD.Reader in = new TaskD.Reader();
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, Reader reader, PrintWriter out) throws IOException{
            int t = reader.nextInt();
            while (t-- > 0) {
                int n = reader.nextInt();
                List<LinkedList<Integer>> segemnts = new ArrayList<>();
                for (int i = 0; i < n - 1; ++i) {
                    LinkedList<Integer> seg = new LinkedList<>();
                    int len = reader.nextInt();
                    for (int j = 0; j < len; ++j) {
                        seg.add(reader.nextInt());
                    }
                    segemnts.add(seg);
                }
                loop:
                for (int i = 1; i <= n; ++i) {
                    List<LinkedList<Integer>> lists = getList(segemnts);
                    List<Integer> res = new ArrayList<>();
                    res.add(i);
                    removeElement(lists, i);
                    for (int k = 1; k <= n - 1; ++k) {
                        int one = count(lists, 1);
                        if (one != 1) {
                            continue  loop;
                        }
                        int nextElement = nextElement(lists);
                        res.add(nextElement);
                        removeElement(lists, nextElement);
                    }

                    next:
                    for (LinkedList<Integer> seg : segemnts) {
                        int len = seg.size();
                        for (int k = 0; k <= res.size() - len; ++k) {
                            List<Integer> sub = res.subList(k, k + len);
                            if (equal(sub, seg)) {
                                continue next;
                            }
                        }
                        continue loop;
                    }
                    res.forEach(e -> out.print(e + " "));
                    out.println();
                    break;
                }
            }
        }

        public boolean equal(List<Integer> list, LinkedList<Integer> linkedList) {

            List<Integer> list1 = new ArrayList<>(linkedList);
            List<Integer> list2 = new ArrayList<>(list);
            Collections.sort(list2);
            Collections.sort(list1);
            return list2.equals(list1);
        }

        public int count(List<LinkedList<Integer>> segments, int len) {
            int count = 0;
            for (LinkedList<Integer> segment : segments) {
                if (segment.size() == len) {
                    ++count;
                }
            }
            return count;
        }

        public int nextElement(List<LinkedList<Integer>> segments) {
            int count = 0;
            for (LinkedList<Integer> segment : segments) {
                if (segment.size() == 1) {
                    return segment.get(0);
                }
            }
            return -1;
        }

        public void removeElement(List<LinkedList<Integer>> segments, int element) {
            int count = 0;
            for (LinkedList<Integer> segment : segments) {
                segment.remove(Integer.valueOf(element));
            }
        }

        public List<LinkedList<Integer>> getList(List<LinkedList<Integer>> segments) {
            List<LinkedList<Integer>> resp = new ArrayList<>();
            for (LinkedList<Integer> linkedList : segments) {
                resp.add(new LinkedList<>(linkedList));
            }
            return resp;
        }

        static class Reader
        {
            final private int BUFFER_SIZE = 1 << 16;
            private DataInputStream din;
            private byte[] buffer;
            private int bufferPointer, bytesRead;

            public Reader()
            {
                din = new DataInputStream(System.in);
                buffer = new byte[BUFFER_SIZE];
                bufferPointer = bytesRead = 0;
            }

            public Reader(String file_name) throws IOException
            {
                din = new DataInputStream(new FileInputStream(file_name));
                buffer = new byte[BUFFER_SIZE];
                bufferPointer = bytesRead = 0;
            }

            public String readLine() throws IOException
            {
                byte[] buf = new byte[64]; // line length
                int cnt = 0, c;
                while ((c = read()) != -1)
                {
                    if (c == '\n')
                        break;
                    buf[cnt++] = (byte) c;
                }
                return new String(buf, 0, cnt);
            }

            public int nextInt() throws IOException
            {
                int ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do
                {
                    ret = ret * 10 + c - '0';
                }  while ((c = read()) >= '0' && c <= '9');

                if (neg)
                    return -ret;
                return ret;
            }

            public long nextLong() throws IOException
            {
                long ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
                if (neg)
                    return -ret;
                return ret;
            }

            public double nextDouble() throws IOException
            {
                double ret = 0, div = 1;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();

                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');

                if (c == '.')
                {
                    while ((c = read()) >= '0' && c <= '9')
                    {
                        ret += (c - '0') / (div *= 10);
                    }
                }

                if (neg)
                    return -ret;
                return ret;
            }

            private void fillBuffer() throws IOException
            {
                bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1)
                    buffer[0] = -1;
            }

            private byte read() throws IOException
            {
                if (bufferPointer == bytesRead)
                    fillBuffer();
                return buffer[bufferPointer++];
            }

            public void close() throws IOException
            {
                if (din == null)
                    return;
                din.close();
            }
        }

    }
}