// 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 int long long
#define ull unsigned long long
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);
    if(f)x=-x;return x;
}

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

#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 500005
#define inf 0x3f3f3f3f

bool isr,isi;
int n,lg,qcnt;
bool a[505][505],res[505][505],b[505][505];

void ask(){
	++qcnt;
	cout<<"?"<<endl;
	For(i,1,n){
		For(j,1,n)cout<<a[i][j];
		cout<<endl;
	}
	int x;cin>>x;
	if(x==1){
		if(!isr){
			while(1);
		}else{
			exit(233);
		}
	}
	For(i,1,n){
		string s;cin>>s;
		For(j,1,n)b[i][j]=(s[j-1]&1),a[i][j]=0;
	}
}
bool hav[505];
bool don[505];

vi buc[505];

void answer(){
	int sum=0;
	For(i,1,n)For(j,1,n)sum+=res[i][j];
	if(sum<n){
		if(isi){
			while(1);
		}
		else assert(0);
	}
	
	cout<<"!"<<endl;
	For(i,1,n){
		For(j,1,n)cout<<res[i][j];
		cout<<endl;
	}
	
	
	int x;cin>>x;
	
//	assert(x==0);
}

vi split(vi o,int l,int r){
	vi p;
	For(i,l,r) p.pb(o[i]);
	return p;
}

void rows(int x){
	isr=1;
	For(i,1,n){
		buc[i].clear();
		For(j,1,n)if(j!=x)buc[i].pb(j);
	//	cout<<"sz "<<buc[i].size()<<"\n";
	}
	while(1){
		bool ok=1;
		For(i,1,n){
			if(!buc[i].size())continue;
			if(buc[i].size()==1){
				res[buc[i][0]][i]=1;
				continue;
			}
			ok=0;
		}
		if(ok){
			answer();
			break;
		}
		For(i,1,n){
			if(buc[i].size()>1){
				int mid=(buc[i].size()-1)>>1;
				a[x][i]=1;
				For(j,mid+1,buc[i].size()-1) a[buc[i][j]][i]=1;
			}
		}
		ask();
		For(i,1,n){
			if(buc[i].size()>1){
				int mid=(buc[i].size()-1)>>1;
				if(b[x][i]) buc[i]=split(buc[i],mid+1,buc[i].size()-1);
				else buc[i]=split(buc[i],0,mid);
			}
		}
	}
}

bool use[505];

void work(int ID)
{
	cin>>n;
	lg=0;qcnt=0;isi=0;
	while((1<<lg)<n)++lg;
	isr=0;
	For(i,1,n)For(j,1,n)res[i][j]=a[i][j]=0;
	For(i,1,n)hav[i]=use[i]=don[i]=0;
//	if(ID==5){
//		For(i,1,n){
//			a[3][i]=1;
//			ask();
//		}exit(0);
//	}
		
	/*
	ABBB
	AABB
	ABAB
	ABBA
	*/
	For(i,1,n)For(j,1,n)if(i==j||j==1)a[i][j]=1;
	a[1][1]=0;
	
	ask();
	if(!b[1][1]){
		rows(1);
		return;
	}
	
	int pos=0;
	For(i,2,n)
		if(!b[i][i])pos=i;
		else hav[i]=1,a[i][1]=1;
	
	bool spe=0;
	if(!pos){
		/*
		BAAA
		ABBB
		ABBB
		ABBB
		*/
		For(i,2,n) a[1][i]=1;
		ask();
		if(b[1][1])res[1][1]=hav[1]=1;
		
		if(hav[1]){
			For(i,2,n) a[i][i]=1;
			ask();
			For(i,2,n) {
				if(b[i][i])res[i][i]=1;
				else res[i][1]=1;
			}
			answer();
			return;
		}
		else spe=1;
	}else{
		a[pos][pos]=a[1][1]=a[1][pos]=1;
		ask();
		For(i,2,n){
			if(!hav[i] && !b[i][1]){
				rows(i);
				return;
			}
		}
		if(b[pos][pos]) res[1][pos]=hav[1]=1;
		else if(b[1][pos]) res[1][1]=hav[1]=1;
		// else : res[1][1]=0
	}
	
	vi o;
	For(i,2,n) if(hav[i]) o.pb(i);
	For(i,2,n) if(!hav[i]) o.pb(i);
	
//	cout<<"o: ";for(auto x:o)cout<<x<<" "; cout<<"\n";
	For(i,1,n) 
		if(!hav[i]) buc[i]=o; else buc[i].clear();
	
	int now=o.size();
	int nw=now;
	For(_,1,lg) nw=(nw+1)>>1;
	assert(nw==1);
	
	while(1){
		bool ok=1;
		int mxs=0;
		For(i,1,n){
			mxs=max(mxs,(int)buc[i].size());
			if(!buc[i].size())continue;
			if(buc[i].size()==1){
				res[i][buc[i][0]]=1;
				continue;
			}
			ok=0;
		}
		if(spe && mxs==2)
		{
			// res[1][1] empty
			int u=buc[1][0],v=buc[1][1];
			if(!don[u] && !don[v]){
				isi=1;
				a[1][1]=1,a[1][u]=1,a[u][1]=1;
				a[v][v]=1;
				ask();
				if(b[v][v]) res[v][v]=1;
				else res[v][1]=1;
				if(b[1][u]) res[1][u]=1;
				else res[1][v]=1;
				if(b[u][1]) res[u][1]=1;
				else res[u][u]=1;
				answer();
				return;
			}
		}
		if(ok){
			bool ok2=1;
			For(i,2,n)
				if(hav[i] && (!res[i][1]&&!res[i][i])) ok2=0;
			if(!ok2){
				For(i,2,n) 
					if(hav[i]) a[i][i]=1;
				ask();
				For(i,2,n)
					if(b[i][i]) res[i][i]=1;
					else res[i][1]=1;
			}
			answer();
			break;
		}
		For(i,1,n) use[i]=0;
		For(i,1,n)
			if(buc[i].size()>1){
				int mid=(buc[i].size()-1)>>1;
				a[i][1]=1;
			//	For(j,mid+1,buc[i].size()-1)cout<<"VIS "<<buc[i][j]<<"\n";
				For(j,mid+1,buc[i].size()-1) a[i][buc[i][j]]=1,use[buc[i][j]]=1;
			}
		For(i,2,n)
			if(hav[i] && !use[i]) a[i][i]=1;
		assert(mxs<=now);
		if(qcnt+1<=lg+2){
			
		}
	//	assert(qcnt+1<=lg+2);
		ask();
		For(i,1,n){
			if(buc[i].size()>1){
				int mid=(buc[i].size()-1)>>1;
				if(b[i][1]) buc[i]=split(buc[i],mid+1,buc[i].size()-1);
				else buc[i]=split(buc[i],0,mid);
			}
		}
		For(i,2,n)
			if(hav[i] && !use[i]){
				if(b[i][i]) res[i][i]=1;
				else res[i][1]=1;
				don[i]=1;
			}
		int mxs2=0;
		For(i,1,n) mxs2=max(mxs2,(int)buc[i].size());
		assert(mxs2<=(mxs+1)/2);
		now=(now+1)/2;
	}
}

signed main()
{
	int T;cin>>T;
	For(_,1,T)work(_);
	return 0;
}
/*
010
111
110

0
100
100
101

1
111
111
101


111
010
010
*/