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#include <cstdio>
#include <algorithm>

using namespace std;

#define D(x)
#define MAX 400

int dis[MAX][MAX],t,n;
char c;
struct P {
    int i,j;
};

P pos[MAX*MAX+10];
int pos_ile=0;

void floyd_warshall() {
    for(int k=0;k<n;k++) {
        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                if (dis[i][j] > dis[i][k] + dis[k][j]) dis[i][j] = dis[i][k] + dis[k][j];
            }
        }
    }
}

void print() {
        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                printf("%d\t", dis[i][j]);
            }
            printf("\n");
        }

}

bool cmp(P x, P y) {
    return dis[x.i][x.j] > dis[y.i][y.j];
}

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

        pos_ile = 0;
        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                scanf(" %c", &c);
                if(c == '1') dis[i][j] = 1;
                else dis[i][j] = MAX*2;
                if (i<j) pos[pos_ile++] = {i,j};
            }
        }
        for(int i=0;i<n;i++) dis[i][i] = 0;
        floyd_warshall();
        D(print();)
        sort(pos, pos+pos_ile, cmp);
        D(for(int i=0;i<pos_ile;i++) printf("(%d,%d):%d ",pos[i].i, pos[i].j, dis[pos[i].i][pos[i].j]);
        printf("\n");)

        int result = dis[pos[0].i][pos[0].j];
        for(int a=0;a<pos_ile;a++) {
            //laczymy pos[a].i <-> pos[a].j
            int x = pos[a].i, y =  pos[a].j;
            int largest = 0;
            for(int b=0;b<pos_ile;b++) {
                int i = pos[b].i, j = pos[b].j;
                int nd = min(dis[i][j], min(dis[i][x], dis[i][y]) + min(dis[x][j], dis[y][j]));
                D(printf("nd: (%d,%d)  %dx%d = %d\n",i,j,x,y,nd);)
                if (largest < nd) largest = nd;
                if (largest >= dis[i][j]) break;
                if (largest >= result) break;
            }
            if (result > largest) result = largest;
        }
        printf("%d\n", result);
    }
}