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#include <bits/stdc++.h>

//#define int long long
#define ll long long
#define ld long double
#define endl '\n'
#define st first
#define nd second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define FOR(i,l,r) for(int i=(l);i<=(r);i++)
#define ROF(i,r,l) for(int i=(r);i>=(l);i--)
using namespace std;
ll infl=1000000000000000007;
int inf=1000000007;
int mod=998244353;
int mod1=998244353;

#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

const int N=407;

int d[N][N];
int mx[N][N][N];
int xd[N][N];

signed main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    srand(2137);
    int tt;
    cin>>tt;
    while(tt--)
    {
		int n;
		cin>>n;
		vector<int>P(n);
		FOR(i,0,n-1) P[i]=i+1;
		random_shuffle(all(P));
		FOR(i,1,n) 
		{
			FOR(j,1,n) 
			{
				char c;
				cin>>c;
				if(c=='1') d[P[i-1]][P[j-1]]=1;
				else d[P[i-1]][P[j-1]]=inf;
				if(i==j) d[P[i-1]][P[j-1]]=0;
			}
		}
		FOR(k,1,n) FOR(i,1,n) FOR(j,1,n) d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
		int ans=0;
		FOR(j,1,n)
		{
			FOR(i,1,n)
			{
				FOR(l,1,n) mx[j][i][d[j][l]]=max(mx[j][i][d[j][l]],d[i][l]);
				ROF(l,n,0) mx[j][i][l]=max(mx[j][i][l],mx[j][i][l+1]);
				ans=max(ans,d[i][j]);
			}
		}
		int l=1,r=n-1,sr;
		while(l<=r)
		{
			sr=(l+r)/2;
			bool is=0;
			FOR(x,1,n)
			{
				FOR(y,1,n)
				{
					xd[x][y]=n+1;
					int L=1,R=n,SR;
					while(L<=R)
					{
						SR=(L+R)/2;
						if(mx[x][y][SR]<=sr)
						{
							xd[x][y]=SR;
							R=SR-1;
						}
						else L=SR+1;
					}
				}
			}
			FOR(x,1,n)
			{
				FOR(y,x+1,n)
				{
					bool ok=1;
					FOR(i,1,n)
					{
						if(d[x][i]<=d[y][i])
						{
							if(d[x][i]>sr||sr-d[x][i]+1<xd[y][i]) 
							{
								ok=0;
								break;
							}
						}
						else
						{
							if(d[y][i]>sr||sr-d[y][i]+1<xd[x][i])
							{
								ok=0;
								break;
							}
						}
						debug(d[x][i]);
					}
					if(ok)
					{
						is=1;
						break;
					}
				}
				if(is) break;
			}
			if(is)
			{
				ans=sr;
				r=sr-1;
			}
			else l=sr+1;
		}
		cout<<ans<<endl;
		FOR(i,1,n) FOR(j,1,n) FOR(l,0,n) mx[i][j][l]=0;
	}
    
    
    return 0;
}