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 $p_l, p_{l + 1}, \dots, p_r$ 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 $t$ ($1 \le t \le 100$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ($2 \le n \le 200$) — 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 $k_i$ ($2 \le k_i \le n$) — 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 $200$ ($\sum n \le 200$).


-----Output-----

For each test case, print the answer: $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$, 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

Difficulty: introductory

Starter code:

Solutions:
import sys
input = sys.stdin.readline

def dfs(x,S):
    #print(x,S)
    for i in range(len(S)):
        if x in S[i]:
            S[i].remove(x)

    #print(x,S)
        
    LEN1=0
    for s in S:
        if len(s)==1:
            LEN1+=1
            ne=list(s)[0]
        if LEN1==2:
            return [-1]
    if LEN1==1:
        return [ne]+dfs(ne,S)
    else:
        return [-1]
    
        
import copy    

t=int(input())
for tests in range(t):
    n=int(input())
    A=tuple(set(list(map(int,input().split()))[1:]) for i in range(n-1))

    for i in range(1,n+1):
        ANS=[i]+dfs(i,copy.deepcopy(A))
        #print(i,ANS)
        if -1 in ANS[:n]:
            continue
        else:
            #print(ANS[:n])
            USE=[0]*(n-1)

            flag=1

            for i in range(n-1,0,-1):
                SET=set()
                for j in range(i,-1,-1):
                    SET.add(ANS[j])
                    if SET in A:
                        break
                else:
                    flag=0
                    break

            if flag:
                print(*ANS[:n])
                break
    

        


def __starting_point():
    t = int(input())
    for _ in range(t):
        n = int(input())
        ns = {}
        for _ in range(n - 1):
            _, *p = list(map(int, input().split()))
            tp = tuple(p)
            for pp in p:
                ns.setdefault(pp, set()).add(tp)
        first = [(k, list(v)[0]) for k, v in list(ns.items()) if len(v) == 1]
        found = False
        while not found:
            nns = {k: v.copy() for k, v in list(ns.items())}
            min_index = {}
            cur, cur_tp = first.pop()
            result = [cur]
            failed = False
            while len(nns) > 0 and not failed:
                nxt = set()
                for k in cur_tp:
                    mi = n - len(result) - len(cur_tp) + 1
                    min_index[k] = max(min_index.get(k, 0), mi)
                    nsk = nns[k]
                    nsk.remove(cur_tp)
                    if k == cur:
                        nns.pop(k)
                    elif len(nsk) == 1:
                        nxt.add(k)
                if len(nns) == len(nxt) or len(nns) == 1:
                    break
                if len(nxt) == 0:
                    failed = True
                else:
                    mmi = -1
                    for nx in nxt:
                        if min_index[nx] > mmi:
                            mmi = min_index[nx]
                            cur = nx
                    cur_tp = list(nns[cur])[0]
                    result.append(cur)
            if not failed:
                found = True
                if len(nns) == 1:
                    result.append(nns.popitem()[0])
                else:
                    a1, a2 = list(nns.keys())
                    if min_index[a1] == 1:
                        result.extend((a1, a2))
                    else:
                        result.extend((a2, a1))
                print(" ".join(map(str, reversed(result))))

__starting_point()

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 = list(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)))


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 = list(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)))


from collections import Counter
from itertools import chain


def dfs(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

    if len(next_r) == 2:
        nr = -1
        can1, can2 = next_r
        for i, h in enumerate(hint_sets):
            if i not in removed:
                continue
            if can1 in h and can2 not in h:
                nr = can1
                break
            if can1 not in h and can2 in h:
                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 = list(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)))


import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def main():
    def ok():
        if len(ans)<n:return False
        for r,si in enumerate(sii,2):
            s=ss[si]
            cur=set(ans[r-len(s):r])
            if s!=cur:return False
        return True

    for _ in range(II()):
        n=II()
        ee=[[n**2]*n for _ in range(n)]
        for ei in range(n):ee[ei][ei]=0
        ss=[set(LI()[1:]) for _ in range(n-1)]
        for a0 in range(1,n+1):
            used=set([a0])
            ans=[a0]
            sii=[]
            for _ in range(n-1):
                nxt=[]
                for si,s in enumerate(ss):
                    cur=s-used
                    if len(cur)==1:
                        for a in cur:nxt.append(a)
                        sii.append(si)
                if len(nxt)!=1:break
                ans.append(nxt[0])
                used.add(nxt[0])
            if ok():break
        print(*ans)

main()

from collections import defaultdict as dd
from pprint import pprint as pp


def solve():
    n = int(input())
    seqs = []
    d = dd(list)
    for _ in range(n-1):
        seqs.append(list(map(int, input().split()[1:])))
    for seq in seqs:
        for i in range(len(seq)):
            s = ' '.join(str(x) for j, x in enumerate(seq) if j != i)
            d[s].append(seq[i])
    for st in range(1, n+1):
        seq = [st]
        seq_set = {st}
        for _ in range(n-1):
            found = False
            for l in range(len(seq)):
                k = ' '.join(str(x) for x in sorted(seq[-(l+1):]))
                if k in d:
                    for j in d[k]:
                        if j not in seq_set:
                            seq.append(j)
                            seq_set.add(j)
                            found = True
                            break
                if found:
                    break
            if not found:
                break
        if len(seq) == n:
            print(' '.join(str(x) for x in seq))
            break


for _ in range(int(input())):
    solve()


import sys
import collections
import threading
import copy

def check(itr, sets):
    d={}
    def dmap(x):
        return d[x]    
    for i in range(len(itr)):
        d[itr[i]] = i
    for perm in sets:
        tmp = sorted(list( map(dmap, perm) ))
        if len(tmp) != tmp[-1] - tmp[0] + 1:
            return False

    return True


def main():
    n = int( input() )
    sets = []
    start = set()
    for _ in range(n-1):
        l, *tmp = list(map( int, input().split() ))
        sets.append( set(tmp) )
        if l == 2:
            start.add(tmp[0])
            start.add(tmp[1])

    ans = collections.deque()
    for i in start:
        permuts = copy.deepcopy(sets)
        next = i
        while len(ans) > 0: ans.pop()

        ans.append(next)
        while len(ans) < n:
            q = []
            for permut in permuts:
                if next in permut:
                    permut.remove(next)
                    if len(permut) == 1:
                        q.append(permut)
            if len(q) != 1:
                break ########## exit
            next = list(q[0])[0]
            ans.append(next)
        if len(ans)==n and check(ans, sets):
            print(*ans)
            return
    print("error")
    return
        

        




input = sys.stdin.readline
#sys.setrecursionlimit(2097152)
tnum = int(input())
for _ in range(tnum):
    main()

# threading.stack_size(134217728)

# main_thread = threading.Thread(target=main)
# main_thread.start()
# main_thread.join()