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#include<bits/stdc++.h>
bool Mbg;
using namespace std;
#define vec vector
#define pb push_back
#define eb emplace_back
#define siz(vec) (int)((vec).size())
#define all(vec) (vec).begin(),(vec).end()
template<class T>
void operator +=(vec<T> &a,T b){a.push_back(b);}
#define pii pair<int,int>
#define x first
#define y second
#define mp make_pair
#define exc(expr) if(expr)continue;
#define stop(expr) if(expr)break;
#define ret(expr) if(expr)return;
#define deb(var) cerr<<#var<<'='<<(var)<<"; "
#define debl(var) cerr<<#var<<'='<<(var)<<";\n"
#define ins insert
#define era erase
#define lb lower_bound
#define ub upper_bound
// #define int long long
// template<class T>
// bool Min(T &x,T y){return x>y?x=y,1:0;}
// template<class T>
// bool Max(T &x,T y){return x<y?x=y,1:0;}
const int mod=998244353;
void Add(int &x,int y){x=x+y<mod?x+y:x+y-mod;}
void Dec(int &x,int y){x=x>=y?x-y:x-y+mod;}
int fpm(int x,int y){
    int ans=1;for(;y;y>>=1,x=1ll*x*x%mod)if(y&1)ans=1ll*x*ans%mod;return ans;
}

#define sh unsigned short
bool Min(sh &x,const sh &y){
    return x>y?x=y,1:0;
}
bool Max(sh &x,const sh &y){
    return x<y?x=y,1:0;
}

sh n;
sh w[410][410],d[410];

void work(){
    cin>>n;
    for(sh i=1;i<=n;i++){
        for(sh j=1;j<=n;j++){
            char ch;
            cin>>ch;
            if(i==j)w[i][j]=0;
            else w[i][j]=ch=='1'?1:n;
        }
    }
    for(sh k=1;k<=n;k++){
        for(sh i=1;i<=n;i++){
            for(sh j=1;j<=n;j++){
                Min(w[i][j],w[i][k]+w[k][j]);
            }
        }
    }

    sh ans=n;
    // int TOT=0;
    for(sh a=1;a<=n;a++){
        for(sh b=a+1;b<=n;b++){
            for(sh u=1;u<=n;u++){
                d[u]=min(w[u][a],w[u][b]);
            }
            sh dis=0;
            bool qt=0;
            for(sh u=1;u<=n;u++){
                for(sh v=u+1;v<=n;v++){
                    // deb(u),debl(v);
                    // ++TOT;
                    if(Max(dis,min(w[u][v],(sh)(d[u]+d[v])))){
                        if(dis>=ans){
                            qt=1;
                            break;
                        }
                    }
                }
                if(qt){
                    break;
                }
            }
            if(!qt){
                ans=dis;
            }
        }
    }
    cout<<ans<<'\n';

    // debl(TOT);
}
bool Med;
signed main(){
    ios::sync_with_stdio(0),
    cin.tie(0),cout.tie(0);
    int T=1;cin>>T;while(T--)work();
    // cerr<<"Time: "<<clock()<<" ms;\n";
    // cerr<<"Memory: "<<abs(&Med-&Mbg)/1024.0/1024.0<<" MiB.\n";
}
/*
- CONTINUE, NON-STOPPING, FOR THE FAITH
- START TYPING IF YOU DON'T KNOW WHAT TO DO
- STOP TYPING IF YOU DON'T KNOW WHAT YOU'RE DOING
*/