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// Author: Bartek Knapik

#include <cstdio>

const int MAX_N = 400+9;

int _min(int a, int b) { return a < b ? a : b; }
int _min(int a, int b, int c) { return _min(a, _min(b, c)); }

struct vec
{
    int count;
    int entries[MAX_N];
    
    void clear() { count = 0; }
    void push(int val) { entries[count++] = val; }
    int &operator[](int pos) { return entries[pos]; }
};

struct path
{
    int k, l, d;
    
    bool operator<(path &oth) { return d > oth.d; }
};

int t;

char input[MAX_N];
vec adj[MAX_N];
int global_dist[MAX_N][MAX_N], dist[MAX_N], q[MAX_N * MAX_N];
path paths[MAX_N*MAX_N], tmp[MAX_N*MAX_N];

void sort(int begin, int end)
{
    if (end - begin <= 1) return;
    
    int mid = (begin + end) / 2;
    
    sort(begin, mid);
    sort(mid, end);
    
    int a = begin;
    int b = mid;
    int c = 0;
    
    while (a < mid && b < end)
    {
        if (paths[a] < paths[b]) tmp[c++] = paths[a++];
        else tmp[c++] = paths[b++];
    }
    
    while (a < mid) tmp[c++] = paths[a++];
    while (b < end) tmp[c++] = paths[b++];
    
    c = 0;
    
    while (begin < end) paths[begin++] = tmp[c++];
}

int get_len(int n, int from, int to)
{
    int qb, qe;
    
    for (int i = 0; i < n; ++i) dist[i] = -1;
    
    qb = qe = 0;
    q[qe++] = from;
    dist[from] = 0;
    
    while (qb - qe)
    {
        int cur = q[qb++];
        for (int i = 0; i < adj[cur].count; ++i)
        {
            if (dist[adj[cur][i]] != -1) continue;
            dist[adj[cur][i]] = 1 + dist[cur];
            if (adj[cur][i] == to)
                return dist[to];
            q[qe++] = adj[cur][i];
        }
    }
}


int solve()
{
    int n, global_ans, ans, tmp_ans, cnt;
    
    scanf("%d", &n);
    
    for (int i = 0; i < n; ++i) adj[i].clear();
    
    for (int i = 0; i < n; ++i)
    {
        scanf("%s", input);
        for (int j = i + 1; j < n; ++j)
        {
            if (input[j] == '1')
            {
                adj[i].push(j);
                adj[j].push(i);
            }
        }
    }
    
    global_ans = MAX_N;
    
    for (int i = 0; i < n; ++i) global_dist[i][i] = 0;
    
    cnt = 0;
    
    for (int i = 0; i < n; ++i)
        for (int j = i + 1; j < n; ++j)
            global_dist[i][j] = global_dist[j][i] = get_len(n, i, j);
        
    for (int i = 0; i < n; ++i)
        for (int j = i + 1; j < n; ++j)
            paths[cnt++] = { i, j, global_dist[i][j] };
    
    sort(0, cnt);
    
    for (int i = 0; i < n; ++i)
        for (int j = i + 1; j < n; ++j)
        {
            ans = 0;
            for (int p = 0; p < cnt; ++p)
            {
                int k = paths[p].k;
                int l = paths[p].l;
                int d = paths[p].d;
                if (d <= ans) break;
                tmp_ans = _min(d, global_dist[k][i] + global_dist[j][l], global_dist[k][j] + global_dist[i][l]);
                if (tmp_ans > ans) ans = tmp_ans;
            }
            if (ans < global_ans) global_ans = ans;
        }
    
    return global_ans;
}

int main()
{
    scanf("%d", &t);
    
    while (t--) printf("%d\n", solve());

    return 0;
}