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/* 2025
 * Maciej Szeptuch
 */
#include <algorithm>
#include <cstdio>

int tests;
int verts;
char edges[512][512];
int dist[512][512];
int dist2[512][512];

int solve(void);
int diameter(int v1, int v2, int best);

int main(void)
{
    scanf("%d", &tests);
    for(int t = 0; t < tests; ++t)
    {
        scanf("%d", &verts);
        for(int v = 0; v < verts; ++v)
            scanf("%s", edges[v]);

        printf("%d\n", solve());
    }

    return 0;
}

int solve(void)
{
    for(int f = 0; f < verts; ++f)
        for(int s = 0; s < verts; ++s)
            if(f != s)
                dist[f][s] = edges[f][s] == '1' ? 1 : 512;

    for(int t = 0; t < verts; ++t)
        for(int f = 0; f < verts; ++f)
            for(int s = 0; s < verts; ++s)
                if(dist[f][s] > dist[f][t] + dist[t][s])
                    dist[f][s] = dist[f][t] + dist[t][s];

    int best = 512;
    for(int f = 0; f < verts; ++f)
        for(int s = f + 1; s < verts; ++s)
            best = std::min(best, diameter(f, s, best));

    return best;
}

int diameter(int v1, int v2, int best)
{
    for(int f = 0; f < verts; ++f)
        for(int s = 0; s < verts; ++s)
            dist2[f][s] = dist[f][s];

    for(int f = 0; f < verts; ++f)
        for(int s = 0; s < verts; ++s)
        {
            if(dist2[f][s] > dist2[f][v1] + dist2[v1][s])
                dist2[f][s] = dist2[f][v1] + dist2[v1][s];

            if(dist2[f][s] > dist2[f][v2] + dist2[v2][s])
                dist2[f][s] = dist2[f][v2] + dist2[v2][s];

            if(dist2[f][s] > dist2[f][v1] + dist2[v2][s])
                dist2[f][s] = dist2[f][v1] + dist2[v2][s];

            if(dist2[f][s] > dist2[f][v2] + dist2[v1][s])
                dist2[f][s] = dist2[f][v2] + dist2[v1][s];

            if(best <= dist2[f][s])
                return best;
        }

    int farthest = 0;
    for(int f = 0; f < verts; ++f)
        for(int s = f + 1; s < verts; ++s)
            farthest = std::max(farthest, dist2[f][s]);

    return farthest;
}