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// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2")
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
//#define int long long
#define SZ(x) ((int)((x).size()))
#define ALL(x) (x).begin(),(x).end()
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	return f?-x:x;
}

#define mod 998244353
struct modint{
	unsigned int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x<o.x?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 505
#define inf 0x3f3f3f3f

int n,dis[maxn][maxn];
char s[maxn];
int c[maxn][maxn],all;
int mx[maxn][maxn],p[maxn][maxn];

void sub(int u,int v){
	if(u>v)swap(u,v);
	if(c[u][v])c[u][v]=0,--all;
}

int ps[maxn],qs[maxn][maxn];
void work(int up){
//	cout<<"work "<<up<<endl;
	For(i,1,n){
		int *p=::p[i];
		while(dis[i][p[ps[i]]]>up){
			int u=p[ps[i]];
			For(j,1,n)
				mx[i][j]=max(mx[i][j],dis[p[j]][u]);
			--ps[i];
		}
		if(ps[i]==n) continue;
		For(j,1,n){
			int v=p[j];
			while(qs[i][j]>=1){
				int u=p[qs[i][j]];
				if(dis[i][u]+mx[i][j]<=up) break;
		//		cout<<"sub "<<i<<" "<<u<<" "<<v<<endl;
				sub(u,v);
				--qs[i][j];
			}
			// dis(i,u) + mx[v] > up: baodiao u
		}
	}
//	For(i,1,n){
//		For(j,i+1,n) cout<<c[i][j]<<" "; cout<<"\n";
//	}
}

void work()
{
	n=read();
	For(i,1,n){
		scanf("%s",s+1);
		For(j,1,n)dis[i][j]=(s[j]&1)?1:inf;
		dis[i][i]=0;
	}
	For(k,1,n)For(i,1,n)For(j,1,n)dis[i][j]=min(dis[i][j],dis[i][k]+dis[k][j]);
	all=0;
	For(i,1,n)For(j,i+1,n)c[i][j]=n,++all;
	For(i,1,n){
		For(j,1,n)p[i][j]=j;
		sort(p[i]+1,p[i]+n+1,[&](int u,int v){
			return dis[i][u]<dis[i][v];
		});
		ps[i]=n;
		For(j,1,n) qs[i][j]=j-1,mx[i][j]=-inf;
	}
	Rep(i,n-1,1){
		work(i);
		if(!all){
			cout<<i+1<<endl;
			return;
		}
	}
	cout<<1<<endl;
}

signed main()
{
	int T=read();
	while(T--)work();
	return 0;
}
/*
2
4
0111
1011
1101
1110
5
01000
10100
01010
00101
00010
*/