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 PYTHON3):

Solution:
from collections import Counter
from itertools import chain


def dfs(n, r, hint_sets, count, removed, result):
    # print(n, r, hint_sets, count, removed, result)
    if len(result) == n - 1:
        last = (set(range(1, n + 1)) - set(result)).pop()
        result.append(last)
        return True

    i, including_r = 0, None
    for i, including_r in enumerate(hint_sets):
        if i in removed:
            continue
        if r in including_r:
            break
    removed.add(i)

    next_r = []
    for q in including_r:
        count[q] -= 1
        if count[q] == 1:
            next_r.append(q)
    if not next_r:
        return False

    # print(r, next_r, result)

    if len(next_r) == 2:
        nr = -1
        can1, can2 = next_r
        for h in hint_sets:
            if can1 in h and can2 not in h and not h.isdisjoint(result):
                nr = can1
                break
            if can1 not in h and can2 in h and not h.isdisjoint(result):
                nr = can2
                break
        if nr == -1:
            nr = can1
    else:
        nr = next_r[0]

    result.append(nr)
    res = dfs(n, nr, hint_sets, count, removed, result)
    if res:
        return True
    result.pop()

    for q in including_r:
        count[q] += 1

    return False


t = int(input())
buf = []
for l in range(t):
    n = int(input())
    hints = []
    for _ in range(n - 1):
        k, *ppp = map(int, input().split())
        hints.append(ppp)

    count = Counter(chain.from_iterable(hints))
    most_common = count.most_common()

    hint_sets = list(map(set, hints))

    r = most_common[-1][0]
    result = [r]
    if dfs(n, r, hint_sets, dict(count), set(), result):
        buf.append(' '.join(map(str, result[::-1])))
        continue
    r = most_common[-2][0]
    result = [r]
    assert dfs(n, r, hint_sets, dict(count), set(), result)
    buf.append(' '.join(map(str, result[::-1])))

print('\n'.join(map(str, buf)))