cp/codeforces/1017/c.cc

#include <bits/stdc++.h>  // {{{

// https://codeforces.com/blog/entry/96344

#pragma GCC optimize("O2,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

using namespace std;

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f64 = double;
using f128 = long double;
//  }}}

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;

// https://mirror.codeforces.com/blog/entry/124683

namespace hashing {
using i64 = std::int64_t;
using u64 = std::uint64_t;
static const u64 FIXED_RANDOM =
    std::chrono::steady_clock::now().time_since_epoch().count();

#if USE_AES
std::mt19937 rd(FIXED_RANDOM);
const __m128i KEY1{(i64)rd(), (i64)rd()};
const __m128i KEY2{(i64)rd(), (i64)rd()};
#endif

template <class T, class D = void>
struct custom_hash {};

template <class T>
inline void hash_combine(u64 &seed, T const &v) {
  custom_hash<T> hasher;
  seed ^= hasher(v) + 0x9e3779b97f4a7c15 + (seed << 12) + (seed >> 4);
};

template <class T>
struct custom_hash<T,
                   typename std::enable_if<std::is_integral<T>::value>::type> {
  u64 operator()(T _x) const {
    u64 x = _x;
#if USE_AES
    __m128i m{i64(u64(x) * 0xbf58476d1ce4e5b9u64), (i64)FIXED_RANDOM};
    __m128i y = _mm_aesenc_si128(m, KEY1);
    __m128i z = _mm_aesenc_si128(y, KEY2);
    return z[0];
#else
    x += 0x9e3779b97f4a7c15 + FIXED_RANDOM;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
#endif
  }
};

template <class T>
struct custom_hash<T, std::void_t<decltype(std::begin(std::declval<T>()))>> {
  u64 operator()(T const &a) const {
    u64 value = FIXED_RANDOM;
    for (auto &x : a)
      hash_combine(value, x);
    return value;
  }
};

template <class... T>
struct custom_hash<std::tuple<T...>> {
  u64 operator()(const std::tuple<T...> &a) const {
    u64 value = FIXED_RANDOM;
    std::apply(
        [&value](T const &...args) {
          (hash_combine(value, args), ...);
        },
        a);
    return value;
  }
};

template <class T, class U>
struct custom_hash<std::pair<T, U>> {
  u64 operator()(std::pair<T, U> const &a) const {
    u64 value = FIXED_RANDOM;
    hash_combine(value, a.first);
    hash_combine(value, a.second);
    return value;
  }
};
};  // namespace hashing

#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class Key, class Value = null_type>
using hashtable = gp_hash_table<
    Key, Value, hashing::custom_hash<Key>, std::equal_to<Key>,
    direct_mask_range_hashing<>, linear_probe_fn<>,
    hash_standard_resize_policy<hash_exponential_size_policy<>,
                                hash_load_check_resize_trigger<>, true>>;

#endif
#ifdef PB_DS_TREE_POLICY_HPP
template <typename T>
using multitree = tree<T, null_type, std::less_equal<T>, rb_tree_tag,
                       tree_order_statistics_node_update>;
template <class Key, class Value = null_type>
using rbtree = tree<Key, Value, std::less<Key>, rb_tree_tag,
                    tree_order_statistics_node_update>;
#endif

void solve() {
  int n;
  cin >> n;
  vector<vector<int>> grid((size_t)n, vector<int>(size_t(n)));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      cin >> grid[i][j];
    }
  }

  vector<int> ans(2 * size_t(n) + 1, 0);
  hashtable<int> seen;

  for (int k = 2; k <= 2 * n; ++k) {
    int x = -1, good = 1;
    for (int i = 1; i <= n; ++i) {
      int j = k - i;
      if (j >= 1 && j <= n) {
        if (x == -1) {
          x = grid[i - 1][j - 1];
        } else if (grid[i - 1][j - 1] != x) {
          good = 0;
          break;
        }
      }
    }
    if (good && x != -1) {
      ans[k] = x;
      seen.insert(x);
    }
  }

  for (int first_candidate = 1; first_candidate <= 2 * n; ++first_candidate) {
    if (seen.find(first_candidate) == seen.end()) {
      cout << first_candidate << ' ';
      for (size_t i = 2; i <= 2 * n; ++i) {
        cout << ans[i] << ' ';
      }
      cout << '\n';
      return;
    }
  }
}

int main() {  // {{{
  cin.tie(nullptr)->sync_with_stdio(false);
  cin.exceptions(cin.failbit);

  int tc = 1;
  cin >> tc;

  for (int t = 0; t < tc; ++t) {
    solve();
  }

  return 0;
}
// }}}