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 CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:66777216")
#pragma warning(disable : 4996)
#pragma hdrstop
static constexpr long double PI = 3.14159265358979323846;
static constexpr int INF = 0x3f3f3f3f;
static constexpr long double EPS = 1e-9;
static constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
static constexpr int DX[8] = {-1, 0, 1, 0, -1, -1, 1, 1};
static constexpr int DY[8] = {0, 1, 0, -1, -1, 1, 1, -1};
static constexpr size_t kDayMonth[12] = {31, 28, 31, 30, 31, 30,
                                         31, 31, 30, 31, 30, 31};
enum Direction : uint8_t {
  Up,
  Right,
  Down,
  Left,
  UpLeft,
  UpRight,
  DownRight,
  DownLeft,
  North = Up,
  East = Right,
  South = Down,
  West = Left,
  NorthWest = UpLeft,
  NorthEast = UpRight,
  SouthEast = DownRight,
  SouthWest = DownLeft,
  Unknown = 255
};
template <typename T>
inline bool is_equal_to_zero(const T& a) {
  if (std::is_floating_point<T>()) {
    return abs(a) < EPS;
  }
  return a == 0;
}
template <typename T>
inline bool umin(T& a, const T& b) {
  return (b < a ? a = b, true : false);
}
template <typename T>
inline bool umax(T& a, const T& b) {
  return (a < b ? a = b, true : false);
}
namespace std {
template <typename T, typename U>
struct hash<std::pair<T, U>> {
  std::size_t operator()(const std::pair<T, U>& lhs) const {
    return lhs.first * 877117 + lhs.second;
  }
};
}  // namespace std
template <typename T, size_t N>
struct MakeVector {
  template <typename... Args,
            typename R = std::vector<decltype(MakeVector<T, N - 1>::make_vector(
                std::declval<Args>()...))>>
  static R make_vector(size_t first, Args... sizes) {
    auto inner = MakeVector<T, N - 1>::make_vector(sizes...);
    return R(first, inner);
  }
};
template <typename T>
struct MakeVector<T, 1> {
  template <typename R = std::vector<T>>
  static R make_vector(std::size_t size, const T& value) {
    return R(size, value);
  }
};
template <typename T, typename... Args>
auto make_vector(Args... args)
    -> decltype(MakeVector<T, sizeof...(Args) - 1>::make_vector(args...)) {
  return MakeVector<T, sizeof...(Args) - 1>::make_vector(args...);
}
template <typename T>
inline bool is_leap_year(const T year) {
  return year % 400 == 0 || (year % 100 != 0 && (year & 3) == 0);
}
inline size_t get_days_in_month(const size_t month, const size_t year) {
  return kDayMonth[month] + (month == 1 && is_leap_year(year) ? 1 : 0);
}
template <typename T,
          typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
class SafeIntegralHash {
 public:
  const T kRandomValue = static_cast<T>(
      std::chrono::high_resolution_clock::now().time_since_epoch().count());
  T operator()(const T& value) const { return value ^ kRandomValue; }
};
template <typename Key, typename Value,
          typename std::enable_if<std::is_integral<Key>::value>::type* =
              nullptr>
using SafeUnorderedMap = std::unordered_map<Key, Value, SafeIntegralHash<Key>>;
template <typename Key, typename Value,
          typename std::enable_if<std::is_integral<Key>::value>::type* =
              nullptr>
using SafeUnorderedMultiMap =
    std::unordered_multimap<Key, Value, SafeIntegralHash<Key>>;
template <typename Key,
          typename std::enable_if<std::is_integral<Key>::value>::type* =
              nullptr>
using SafeUnorderedSet = std::unordered_set<Key, SafeIntegralHash<Key>>;
template <typename Key,
          typename std::enable_if<std::is_integral<Key>::value>::type* =
              nullptr>
using SafeUnorderedMultiSet =
    std::unordered_multiset<Key, SafeIntegralHash<Key>>;
template <bool... Bools>
struct Disjunction : std::false_type {};
template <bool First, bool... Others>
struct Disjunction<First, Others...>
    : std::integral_constant<bool, First || Disjunction<Others...>::value> {};
template <typename T>
constexpr auto has_begin(int) -> decltype(std::begin(std::declval<T>()), true) {
  return true;
}
template <typename T>
constexpr bool has_begin(...) {
  return false;
}
template <typename T>
using is_container = std::integral_constant<bool, has_begin<T>(0)>;
template <typename T, typename... Types>
using is_one_of = Disjunction<std::is_same<T, Types>::value...>;
template <typename T>
using is_sane_integer = std::integral_constant<
    bool,
    std::is_integral<T>::value &&
        !is_one_of<typename std::remove_cv<T>::type, char, signed char,
                   unsigned char, bool, char16_t, char32_t, wchar_t>::value>;
std::string to_string(const std::string& s) { return '"' + s + '"'; }
std::string to_string(const char* s) { return to_string(std::string(s)); }
std::string to_string(const char ch) { return {'\'', ch, '\''}; }
std::string to_string(const bool b) { return (b ? "true" : "false"); }
template <typename T,
          typename std::enable_if<Disjunction<
              is_sane_integer<T>::value,
              std::is_floating_point<T>::value>::value>::type* = nullptr>
std::string to_string(const T value) {
  return std::to_string(value);
}
template <typename A, typename B>
std::string to_string(const std::pair<A, B>&);
template <typename T,
          typename std::enable_if<is_container<T>::value>::type* = nullptr>
std::string to_string(const T& container) {
  bool is_first = true;
  std::string res = "{";
  for (const auto& x : container) {
    if (!is_first) {
      res += ", ";
    }
    is_first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
std::string to_string(const std::pair<A, B>& p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
std::vector<std::string> vec_splitter(std::string s) {
  s += ',';
  std::vector<std::string> res;
  while (!s.empty()) {
    res.push_back(s.substr(0, s.find(',')));
    s = s.substr(s.find(',') + 1);
  }
  return res;
}
void debug_out(std::vector<std::string> __attribute__((unused)) args,
               __attribute__((unused)) int idx,
               __attribute__((unused)) int LINE_NUM) {
  std::cerr << std::endl;
}
template <typename Head, typename... Tail>
void debug_out(std::vector<std::string> args, int idx, int LINE_NUM, Head H,
               Tail... T) {
  std::stringstream ss;
  ss << to_string(H);
  if (idx > 0) {
    std::cerr << ", ";
  } else {
    std::cerr << "Line(" << LINE_NUM << ") ";
  }
  std::cerr << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, LINE_NUM, T...);
}
namespace std {
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& vec) {
  for (auto& it : vec) {
    in >> it;
  }
  return in;
}
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& rhs) {
  in >> rhs.first >> rhs.second;
  return in;
}
}  // namespace std
void assign_files_input_txt() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
template <typename T>
class IntegerIterator
    : public std::iterator<std::input_iterator_tag, T, std::ptrdiff_t, T*, T> {
 public:
  using value_type = T;
  constexpr explicit IntegerIterator(const value_type value) : value_(value) {}
  IntegerIterator& operator++() {
    ++value_;
    return *this;
  }
  IntegerIterator operator++(int) {
    IntegerIterator copy = *this;
    ++value_;
    return copy;
  }
  IntegerIterator& operator--() {
    --value_;
    return *this;
  }
  IntegerIterator operator--(int) {
    IntegerIterator copy = *this;
    --value_;
    return copy;
  }
  constexpr value_type operator*() const { return value_; }
  constexpr bool operator==(const IntegerIterator rhs) const {
    return value_ == rhs.value_;
  }
  constexpr bool operator!=(const IntegerIterator rhs) const {
    return !(*this == rhs);
  }
  constexpr value_type operator+(const IntegerIterator rhs) const {
    return value_ + rhs.value_;
  }
  IntegerIterator& operator+=(const IntegerIterator rhs) const {
    value_ += rhs.value_;
    return *this;
  }
  constexpr value_type operator-(const IntegerIterator rhs) const {
    return value_ - rhs.value_;
  }
  IntegerIterator& operator-=(const IntegerIterator rhs) const {
    value_ -= rhs.value_;
    return *this;
  }

 private:
  value_type value_;
};
template <typename T>
class IntegerRange {
 public:
  using const_iterator = IntegerIterator<T>;
  constexpr IntegerRange(const T begin, const T end)
      : begin_(begin), end_(end) {}
  constexpr const_iterator begin() const { return const_iterator(begin_); }
  constexpr const_iterator end() const { return const_iterator(end_); }
  constexpr T size() const { return end_ - begin_; }

 private:
  T begin_;
  T end_;
};
template <typename T>
class ReversedIntegerRange {
 public:
  using const_iterator = IntegerIterator<T>;
  using reverse_iterator = std::reverse_iterator<const_iterator>;
  constexpr ReversedIntegerRange(const T begin, const T end)
      : begin_(begin), end_(end) {}
  constexpr reverse_iterator begin() const {
    return reverse_iterator(const_iterator(begin_));
  }
  constexpr reverse_iterator end() const {
    return reverse_iterator(const_iterator(end_));
  }
  constexpr T size() const { return end_ - begin_; }

 private:
  T begin_;
  T end_;
};
template <typename T>
constexpr IntegerRange<T> range(const T to) {
  return IntegerRange<T>(0, to);
}
template <typename T>
constexpr IntegerRange<T> range(const T from, const T to) {
  return IntegerRange<T>(from, to);
}
template <typename T>
constexpr IntegerRange<T> inclusiveRange(const T to) {
  return IntegerRange<T>(0, to + 1);
}
template <typename T>
constexpr IntegerRange<T> inclusiveRange(const T from, const T to) {
  return IntegerRange<T>(from, to + 1);
}
template <typename T>
constexpr ReversedIntegerRange<T> downrange(const T from) {
  return ReversedIntegerRange<T>(from, 0);
}
template <typename T>
constexpr ReversedIntegerRange<T> downrange(const T from, const T to) {
  return ReversedIntegerRange<T>(from, to);
}
template <typename T>
constexpr ReversedIntegerRange<T> inclusiveDownrange(const T from) {
  return ReversedIntegerRange<T>(from + 1, 0);
}
template <typename T>
constexpr ReversedIntegerRange<T> inclusiveDownrange(const T from, const T to) {
  return ReversedIntegerRange<T>(from + 1, to);
}
template <typename R>
void sort(R& range) {
  std::sort(range.begin(), range.end());
}
template <typename R, typename Comp>
void sort(R& range, Comp comp) {
  std::sort(range.begin(), range.end(), comp);
}
template <typename R>
void reverse(R& range) {
  std::reverse(range.begin(), range.end());
}
template <typename R, typename T>
auto lower_bound(const R& range, const T& value) -> decltype(range.begin()) {
  return std::lower_bound(range.begin(), range.end(), value);
}
template <typename R, typename T, typename Comp>
auto lower_bound(const R& range, const T& value, Comp comp)
    -> decltype(range.begin()) {
  return std::lower_bound(range.begin(), range.end(), value, comp);
}
template <typename R, typename T>
auto upper_bound(const R& range, const T& value) -> decltype(range.begin()) {
  return std::upper_bound(range.begin(), range.end(), value);
}
template <typename R, typename T, typename Comp>
auto upper_bound(const R& range, const T& value, Comp comp)
    -> decltype(range.begin()) {
  return std::upper_bound(range.begin(), range.end(), value, comp);
}
template <typename R>
auto min_element(const R& range) -> decltype(range.begin()) {
  return std::min_element(range.begin(), range.end());
}
template <typename R>
auto max_element(const R& range) -> decltype(range.begin()) {
  return std::max_element(range.begin(), range.end());
}
template <typename R>
bool next_permutation(R& range) {
  return std::next_permutation(range.begin(), range.end());
}
template <typename T>
void unique(std::vector<T>& range) {
  range.erase(std::unique(range.begin(), range.end()), range.end());
}
template <typename R>
R sorted(R range) {
  sort(range);
  return range;
}
template <typename R, typename Comp>
R sorted(R range, Comp comp) {
  sort(range, comp);
  return range;
}
template <typename R>
R reversed(R range) {
  reverse(range);
  return range;
}
class FVosstanovitPerestanovkuPoOtsortirovannimOtrezkam {
 public:
  void solve(std::istream& in, std::ostream& out) {
    int tests_count = 0;
    in >> tests_count;
    for (int test_id : range(tests_count)) {
      int n;
      in >> n;
      auto a = make_vector<int>(n - 1, 0, 0);
      std::vector<SafeUnorderedSet<int>> sets;
      for (int i : range(n - 1)) {
        int m;
        in >> m;
        a[i] = make_vector<int>(m, 0);
        in >> a[i];
        for (int& x : a[i]) {
          --x;
        }
        sets.emplace_back(a[i].begin(), a[i].end());
      }
      auto resolve = [&a, &sets, n, &out](const int x, const int y,
                                          const int start_pair_index) {
        std::vector<int> p(n, -1);
        p[0] = x;
        p[1] = y;
        SafeUnorderedSet<int> start_pair_set = sets[start_pair_index];
        std::vector<bool> used(n - 1, false);
        used[start_pair_index] = true;
        42;
        for (int p_ind : range(2, n)) {
          std::vector<std::pair<int, int>> candidates;
          for (int i : range(n - 1)) {
            if (used[i]) {
              continue;
            }
            auto cur_set = sets[i];
            for (int j : downrange(p_ind)) {
              auto it = cur_set.find(p[j]);
              if (it == cur_set.cend()) {
                break;
              } else {
                cur_set.erase(it);
              }
            }
            42;
            if (cur_set.size() != 1) {
              continue;
            }
            const int remaining_element = *cur_set.begin();
            if (start_pair_set.find(remaining_element) !=
                start_pair_set.cend()) {
              continue;
            }
            candidates.emplace_back(i, remaining_element);
          }
          42;
          if (candidates.size() != 1) {
            return false;
          }
          const int vec_ind = candidates.front().first;
          const int element = candidates.front().second;
          used[vec_ind] = true;
          p[p_ind] = element;
        }
        for (int x : p) {
          out << x + 1 << " ";
        }
        out << std::endl;
        return true;
      };
      bool found = false;
      for (int start_pair_index : range(n)) {
        const auto& start_pair = a[start_pair_index];
        if (start_pair.size() > 2) {
          continue;
        }
        42;
        if (resolve(start_pair.front(), start_pair.back(), start_pair_index) ||
            resolve(start_pair.back(), start_pair.front(), start_pair_index)) {
          found = true;
          break;
        }
      }
      assert(found);
    }
  }
  bool check(std::string input, std::string expected_output,
             std::string actual_output) {
    return true;
  }
  static constexpr size_t kGeneratedTestsCount = 0;
  static void generate_test(std::ostream& test) {}

 private:
  size_t test_id_ = 0;
};
int main() {
  FVosstanovitPerestanovkuPoOtsortirovannimOtrezkam solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  srand(time(nullptr));
  out << std::fixed << std::setprecision(16);
  solver.solve(in, out);
  return 0;
}