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#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,abm,mmx,tune=native")
//#pragma clang diagnostic ignored "-Wunused-const-variable"
#include<vector>
#include<iostream>
#include<stack>
#include<cmath>
#include<algorithm>
#include<set>
#include<map>
#include<string>
#include<tuple>
#include<bitset>
#include<queue>
#include<unordered_map>
#include<unordered_set>
#include<random>
#include<assert.h>
#include<ctime>
#include <cassert>
#include <thread>
#include <mutex>
#include <semaphore>
#include <chrono>
//#define int long long
#define all(a) a.begin(), a.end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
using namespace std;
ll gcd(ll i, ll j) {
	if (i < j)swap(i, j);
	if (j == 0)return i;
	else return gcd(j, i % j);
}
#ifdef _MY
ll __builtin_popcount(ll x) { return x ? (__builtin_popcount(x >> 1) + (x & 1)) : 0; }
#endif
template<typename T> inline T getint() {
	T val = 0;
	char c;

	bool neg = false;
	while ((c = getchar()) && !(c >= '0' && c <= '9')) {
		neg |= c == '-';
	}

	do {
		val = (val * 10) + c - '0';
	} while ((c = getchar()) && (c >= '0' && c <= '9'));

	return val * (neg ? -1 : 1);
}
const ll INF = 1e7 + 100;
const int mod = 998244353, mod1 = 1000000007;
const ld eps = 1e-7, pi = acos(-1);
const int maxT = 503, maxN = 1 << 22, A = 311;
ll bp(ll et, ll b) {
	ll res = 1;
	for (int i = 30; i >= 0; --i) {
		res = (res * res) % mod;
		if ((b & (1 << i)) != 0)res = (res * et) % mod;
	}
	return res;
}
mt19937 mt_rand(time(0));
void panic() {
	cout << "No\n";
	exit(0);
}
ld get_time() {
	ll tmr = clock();
	return (ld)tmr / CLOCKS_PER_SEC;
}
int pl(int a, int b) {
	a += b;
	if (a >= mod)
		a -= mod;
	return a;
}
int mul(ll a, ll b) {
	return a * b % mod;
}

void solve() {
	int n;
	cin >> n;
	vector<vector<int>>arr(n, vector<int>(n));
	for (int i = 0; i < n; ++i) {
		string s;
		//(n,'1');
		cin >> s;
		for (int j = 0; j < n; ++j) {
			if (i == j) {
				arr[i][j] = 0;
			}
			else {
				if (s[j] == '0') {
					arr[i][j] = INF;
				}
				else {
					arr[i][j] = 1;
				}
			}
		}
	}
	vector<tuple<int, int, int>>arr2;
	for (int m = 0; m < n; ++m) {
		for (int a = 0; a < n; ++a) {
			for (int b = 0; b < n; ++b) {
				arr[a][b] = min(arr[a][b], arr[a][m] + arr[m][b]);
			}
		}
	}
	for (int a = 0; a < n; ++a) {
		for (int b = a+1; b < n; ++b) {
			arr2.push_back({ arr[a][b],a,b });
		}
	}
	sort(arr2.begin(), arr2.end());
	reverse(all(arr2));
	int ans = INF;
	for (int f = 0; f < n; ++f) {
		for (int s = f + 1; s < n; ++s) {
			int tmpcost = 0;
			for (const auto& x : arr2) {
				int cs, a, b;
				tie(cs, a, b) = x;
				if (cs <= tmpcost) {
					break;
				}
				cs = min(arr[a][b], min(
					arr[a][f] + arr[s][b],
					arr[a][s] + arr[f][b]
				));
				tmpcost = max(tmpcost, cs);
			}
			ans = min(ans, tmpcost);
		}
	}
	cout << ans << "\n";
}
int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cout.precision(20);
#ifdef _MY
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);


	/*time_t start, end;
	time(&start);*/
#else
	//freopen("epic.in", "r", stdin); freopen("epic.out", "w", stdout);
#endif
   // init();
	int t = 1;
	cin >> t;
	while (t--) {
		solve();
	}
#ifdef _MY
	cout << "Time taken is : " << fixed << get_time() << " sec " << "\n";
#endif
	return 0;
}