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#pragma GCC optimize ("Ofast")
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define FOR(i, a, b) for (auto i=(a); i<(b); i++)
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(), (x).end()
#ifdef DEBUG
#include "debug.h"
#else
#define dbg(...) 0
#endif

const int maxN = 402;

std::bitset <maxN> G[maxN], distants;
int n, dist[maxN][maxN], Q[maxN][maxN], qBack[maxN];

std::vector <int> bucket[maxN];
int key[maxN];

void bfs(int src, int D[maxN], int que[maxN], int& qb)
{
	std::fill(D, D + n, n);
	qb = 0;
	
	auto push = [&](int v, int d) {
		D[v] = d;
		que[qb++] = v;
	};

	push(src, 0);
	FOR(qf, 0, n-1)
	{
		int v = que[qf];
		FOR(u, 0, n)
			if (G[v].test(u) and D[u] == n)
				push(u, D[v] + 1);
	}
}

void precalc()
{
	FOR(src, 0, n)
		bfs(src, dist[src], Q[src], qBack[src]);
	FOR(src, 0, n)
		G[src].set();
}

void bucketSort(std::vector <int>& I)
{
	for (int& i : I)
		bucket[key[i]].push_back(i);
	I.clear();

	FOR(k, 0, n)
	{
		I.insert(I.end(), ALL(bucket[k]));
		bucket[k].clear();
	}
}

void restrictGraph(int tank)
{
	FOR(v, 0, n)
	{
		int u;
		while (u = Q[v][qBack[v] - 1], dist[v][u] > tank)
		{
			G[v].reset(u);
			--qBack[v];
			assert(qBack[v] > 0);
		}
	}
}

bool check(const std::vector <int>& inds, int tank)
{
	auto isSubset = [&](const std::bitset<maxN>& sub, const std::bitset<maxN>& over) {
		return sub == (sub & over);
	};
	restrictGraph(tank);
	distants.reset();
	auto backIter = inds.rbegin();

	for (int i : inds)
	{
		while (backIter != inds.rend() and key[i] + key[*backIter] > tank)
			distants.set(*backIter++);
		if (not isSubset(distants, G[i]))
			return false;
	}
	return true;
}

void solve()
{
	scanf ("%d", &n);
	
	FOR(i, 0, n)
	{
		char buff[maxN];
		scanf ("%s", buff);
		std::reverse(buff, buff + n);
		G[i] = std::bitset<maxN>(buff);
	}

	precalc();
	std::vector <int> inds(n);
	std::iota(ALL(inds), 0);
	int tank = n;

	FOR(a, 1, n) FOR(b, 0, a)
	{
		FOR(v, 0, n)
			key[v] = std::min(dist[a][v], dist[b][v]);
		bucketSort(inds);

		while (check(inds, tank))
			--tank;
	}

	printf("%d\n", tank + 1);
}

int main()
{
	int tc = 1;
	scanf ("%d", &tc);	
	FOR(cid, 1, tc+1)
		solve();
	return 0;
}