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#include <bits/stdc++.h>
using namespace std;
// #define DEBUG

#define ff first
#define ss second
#define pb push_back
#define eb emplace_back

#define FASTIO                                                                 \
  std::ios::sync_with_stdio(false);                                            \
  cin.tie(NULL);

#ifdef DEBUG
#define debug(x) cerr << #x << " = " << x << endl;
#else
#define debug(x)
#endif

using ll = long long;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vs = vector<string>;

#define ifor(x) for (int i = 0; i < x; i++)
#define vcin(v, n)                                                             \
  ifor(n) {                                                                    \
    int abc;                                                                   \
    cin >> abc;                                                                \
    v.push_back(abc);                                                          \
  }

void ld(int *container, int n) {
  for (int i = 0; i < n; i++) {
    cin >> *(container + i);
  }
}

class Path {
public:
  int x, y, w;
  Path(int x, int y, int w) : x(x), y(y), w(w){};
};

pair<vvi, vvi> floydWarshall(vvi dis) {
  int V = dis.size();
  vvi next = vector<vector<int>>(dis.size(), vector<int>(dis.size(), 0));
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) {
      if (dis[i][j] == -1)
        next[i][j] = -1;
      else
        next[i][j] = j;
    }
  }
  ///
  for (int k = 0; k < V; k++) {
    for (int i = 0; i < V; i++) {
      for (int j = 0; j < V; j++) {
        if ((dis[i][j] == -1 || dis[i][j] > (dis[i][k] + dis[k][j])) &&
            (dis[k][j] != -1 && dis[i][k] != -1)) {
          dis[i][j] = dis[i][k] + dis[k][j];
          next[i][j] = next[i][k];
        }
        /*if (dis[i][k] == -1 || dis[k][j] == -1)
          continue;

        if (dis[i][j] > dis[i][k] + dis[k][j]) {
          dis[i][j] = dis[i][k] + dis[k][j];
          next[i][j] = next[i][k];
        }*/
      }
    }
  }
  return {dis, next};
}

vi constructPath(int u, int v, vvi &next) {
  if (next[u][v] == -1)
    return {};
  vector<int> path = {u};
  while (u != v) {
    u = next[u][v];
    path.push_back(u);
  }
  return path;
}

Path srednica(vector<vector<int>> &g_fw) {
  pair<int, int> longestPath = {-1, -1};
  int longestWeight = -1;
  for (int i = 0; i < g_fw.size(); i++) {
    for (int j = 0; j < g_fw[i].size(); j++) {
      int x = g_fw[i][j];
      if (x > longestWeight && i != j) {
        longestWeight = x;
        longestPath = {i, j};
      }
    }
  }
  return Path(longestPath.first, longestPath.second, longestWeight);
}

vector<Path> srednica_pozostale(vector<vector<int>> &g_fw, Path &p) {
  pair<int, int> longestPath = {p.x, p.y};
  int longestWeight = p.w;
  vector<Path> result;
  for (int i = 0; i < g_fw.size(); i++) {
    for (int j = 0; j < g_fw[i].size(); j++) {
      int x = g_fw[i][j];
      if (x >= longestWeight && i != j && !(p.x == i && p.y == j) &&
          !(p.x == j && p.y == i)) {
        longestWeight = x;
        longestPath = {i, j};
        result.pb(Path(longestPath.first, longestPath.second, longestWeight));
      }
    }
  }
  return result;
}

int calcBajtobenzyna(vector<vector<int>> &g_fw) {
  pair<int, int> longestPath = {-1, -1};
  int longestWeight = -1;
  for (int i = 0; i < g_fw.size(); i++) {
    for (int j = 0; j < g_fw[i].size(); j++) {
      int x = g_fw[i][j];
      if (x > longestWeight && i != j) {
        longestWeight = x;
        longestPath = {i, j};
      }
    }
  }
  return longestWeight;
}

/*vi get_ecc(vvi &g_fw) {
  vi max_val;
  for (auto v : g_fw) {
    int local_max = -1;
    for (auto w : v) {
      local_max = max(w, local_max);
    }
    max_val.push_back(local_max);
  }
  return max_val;
}

int koszt_z_teleportem(vvi &g_fw, int x, int y) {
  auto ecc = get_ecc(g_fw);
  int max_koszt = ecc[0];
  for (int i = 0; i < ecc.size(); i++) {
    max_koszt = min(min(g_fw[i][x] + 1, g_fw[i][y] + 1), max_koszt);
  }
  return max_koszt;
}*/

int koszt_z_teleportem(vvi &g_fw, int x, int y) {
  int max_koszt = 0;
  for (int i = 0; i < g_fw.size(); i++) {
    for (int j = i + 1; j < g_fw.size(); j++) {
      int new_koszt = min(min(g_fw[i][j], g_fw[i][x] + g_fw[y][j]),
                          g_fw[i][y] + g_fw[x][j]);
      max_koszt = max(max_koszt, new_koszt);
    }
  }
  return max_koszt;
}

vector<Path> get_wszystkie_srednice(vvi &g_fw) {
  auto pierwsza = srednica(g_fw);
  auto pozostale = srednica_pozostale(g_fw, pierwsza);
  pozostale.pb(pierwsza);
  return pozostale;
}

vector<vector<bool>> ALREADY_CALCULATED;

int koszt_dla_sredn(vvi &g_fw, Path &sredn, vi &sredn_sc) {
  int max_koszt = sredn.w;
  for (int i = 0; i < sredn_sc.size(); i++) {
    for (int j = i + 1; j < sredn_sc.size(); j++) {
      if (j == i)
        continue;
      // ALREADY_CALCULATED[i][j] = 1;
      //  ALREADY_CALCULATED[j][i] = 1;
      int new_koszt = koszt_z_teleportem(g_fw, sredn_sc[i], sredn_sc[j]);
      max_koszt = min(max_koszt, new_koszt);
    }
  }
  return max_koszt;
}

/*set<int> znajdz_najbardziej_oddalone(vvi &g_fw) {
  set<int> result;
  vi max_val;
  for (auto v : g_fw) {
    int local_max = -1;
    for (auto w : v) {
      local_max = max(w, local_max);
    }
    max_val.push_back(local_max);
  }
  int global_max = -1;
  for (auto v : max_val) {
    global_max = max(v, global_max);
  }
  for (int i = 0; i < max_val.size(); i++) {
    if (max_val[i] == global_max) {
      result.insert(i);
    }
  }
  return result;
}*/
#define BRUTE
int calc(vector<vector<int>> &g) {
  ALREADY_CALCULATED =
      vector<vector<bool>>(g.size(), vector<bool>(g.size(), 0));
  auto [g_fw, next] = floydWarshall(g);
  auto srednice = get_wszystkie_srednice(g_fw);

  int max_koszt = srednice[0].w;

  set<int> wszystkie;
  for (auto sredn : srednice) {
    auto sredn_sc = constructPath(sredn.x, sredn.y, next);
    for (auto v : sredn_sc) {
      wszystkie.insert(v);
    }
  }
#ifdef BRUTE
  for (int i = 0; i < g.size(); i++)
    wszystkie.insert(i);
#endif
  /*for (int i = 0; i < g.size(); i++) {
    int local_max = -1;
    for (int j = 0; j < g.size(); j++) {
      if (g_fw[i][j] > local_max)
        local_max = g_fw[i][j];
    }
    if (local_max < max_koszt - 2)
      wszystkie.erase(i);
  }*/
  // wszystkie.merge(znajdz_najbardziej_oddalone(g_fw));
  vector<int> sredn_sc(wszystkie.begin(), wszystkie.end());
  // cout << "COUNT: " << sredn_sc.size() << "\n";
  auto koszt = koszt_dla_sredn(g_fw, srednice[0], sredn_sc);
  max_koszt = min(max_koszt, koszt);
  return max_koszt;
}
/*
for (int i = 0; i < srednice.size(); i++) {
  auto sredn = srednice[i];
  auto sredn_sc = constructPath(sredn.x, sredn.y, next);
  auto koszt = koszt_dla_sredn(g_fw, sredn, sredn_sc);
  max_koszt = min(max_koszt, koszt);
}
return max_koszt;
}
*/

/**
int calc(vector<vector<int>> &g) {
  auto [g_fw, next] = floydWarshall(g);
  auto sredn = srednica(g_fw);
  auto sredn_sc = constructPath(sredn.x, sredn.y, next);
#ifdef DEBUG
  auto s2 = srednica_pozostale(g_fw, sredn);
  cout << "!!! UWAGA ZNALEZIONO INNE SREDNICE: " << s2.size() << "\n";
  if (sredn.x != s2.x || sredn.y != s2.y) {
    cout << "!!!UWAGA Istnieje inna srednica: x: " << s2.x << "; y: " << s2.y
         << "; w: " << s2.w << "!!!\n";
  }
  cout << "srednica: x: " << sredn.x << "; y: " << sredn.y << "; w: " <<
sredn.w
       << "\n";
#endif
  int max_koszt = sredn.w;


  for (int i = 0; i < sredn_sc.size(); i++) {
#ifdef DEBUG
    cout << "calculating i=" << i << "/" << sredn_sc.size() << "\n";
#endif
    for (int j = i + 1; j < sredn_sc.size(); j++) {
      if (j == i)
        continue;
      int new_koszt = koszt_z_teleportem(g_fw, sredn_sc[i], sredn_sc[j]);
#ifdef DEBUG
      if (new_koszt < max_koszt)
        cout << "!Znaleziono lepszy koszt na odcinku i=" << i << "; j=" << j
             << "; sredn_sc[i]=" << sredn_sc[i]
             << "; sredn_sc[j]=" << sredn_sc[j]
             << "; sredn_sc.size()=" << sredn_sc.size()
             << "; KOSZT=" << new_koszt << ";\n";
#endif
      max_koszt = min(max_koszt, new_koszt);
    }
  }
  return max_koszt;
}*/

int main() {
#ifndef DEBUG
  FASTIO
#endif
  int t; // 1<=t<=21
  cin >> t;

  for (int i = 0; i < t; i++) {
    int n; // 3<=n<=400, l. miast
    cin >> n;
    auto g = vector<vector<int>>(n, vector<int>(n, 0));
    for (int j = 0; j < n; j++) {
      string s;
      cin >> s;
      for (int k = 0; k < n; k++) {
        char x = s[k];
        if (x == '1')
          g[j][k] = 1;
        else if (j == k)
          g[j][k] = 0;
        else
          g[j][k] = -1;
      }
    }
    cout << calc(g) << "\n";
  }
}