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#include <iostream>
#include <cassert>
#include <vector>
#include <algorithm>
#include <bitset>
#include <random>
#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("popcnt")
#define debug(x) #x << " = " << x << '\n'

using ll = long long;
#define YES std::cout << "YES\n"
#define NO std::cout << "NO\n"

const int NMAX = 400;
const int INF = 1e9;

std::mt19937 rng(123);

int n;

int g[NMAX][NMAX];
int d[NMAX][NMAX];

std::bitset<NMAX> who[NMAX][NMAX + 1]; // who[u][x] =def= care sunt nodurile care se afla la distanta cel mult x de u
std::bitset<NMAX> cand;

bool check(int mid) {
  for (int u = 0; u < n; u++) {
		for (int i = 0; i < n; i++) {
			cand[i] = true;
		}
		cand[u] = false;
		for (int i = 0; i < n && cand != 0; i++) {
			for (int j = 0; j < n; j++) {
				if (d[i][j] <= mid) {
					continue;
				}
				if (d[i][u] <= mid && d[j][u] <= mid) {
				  cand &= who[i][mid - d[j][u]] | who[j][mid - d[i][u]];
				} else if (d[i][u] <= mid) {
					cand &= who[j][mid - d[i][u]];
				} else if (d[j][u] <= mid) {
					cand &= who[i][mid - d[j][u]];
				} else {
					cand = 0;
					break;
				}
			}
		}
		if (cand != 0) {
			return true;
		}
  }
	return false;
}

void solve() {
	cand = 0;
	std::cin >> n;

	std::vector<int> p(n);
	for (int i = 0; i < n; i++) {
		p[i] = i;
	}

	std::shuffle(p.begin(), p.end(), rng);

	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			char c;
			std::cin >> c;
			g[p[i]][p[j]] = c - '0';
		}
	}
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (g[i][j] == 1) {
				d[i][j] = 1;
			} else {
				d[i][j] = INF;
			}
		}
		d[i][i] = 0;
	}

	for (int k = 0; k < n; k++) {
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				d[i][j] = std::min(d[i][j], d[i][k] + d[k][j]);
			}
		}
	}

	int maxd = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < i; j++) {
			maxd = std::max(maxd, d[i][j]);
		}
	}

	for (int i = 0; i < n; i++) {
		for (int j = 0; j <= n; j++) {
			who[i][j] = 0;
		}
		for (int j = 0; j < n; j++) {
			who[i][d[i][j]][j] = true;
		}
		for (int j = 1; j <= n; j++) {
			who[i][j] |= who[i][j - 1];
		}
	}

	int l = 1, r = maxd;
	while (l < r) {
		int mid = (l + r) / 2;
		if (check(mid)) {
			r = mid;
		} else {
			l = mid + 1;
		}
	}

	std::cout << r;
}

int main() {
  #ifdef LOCAL
freopen("input.txt", "r", stdin);
  #endif
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(0);

   int t;
   std::cin >> t;
   for (int tc = 1; tc <= t; tc++) {
    solve();
    std::cout << '\n';
   }

  return 0;
}