Advanced Mask, also utilizing the principle of combinations and permutations in DP.
First, let's see if there are any weapons that can kill this enemy without having killed it previously.
//
// GGGGGGGGGGGGG CCCCCCCCCCCCC AAA
// GGG::::::::::::G CCC::::::::::::C A:::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A
// G:::::G GGGGGG C:::::C CCCCCC A:::::::::A
//G:::::G C:::::C A:::::A:::::A
//G:::::G C:::::C A:::::A A:::::A
//G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A
//G:::::G G::::::::GC:::::C A:::::A A:::::A
//G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A
//G:::::G G::::GC:::::C A:::::::::::::::::::::A
// G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A
// GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A
// GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define debug(...) printf("DEBUG: "),printf(__VA_ARGS__)
#define gettime() end_time=clock();printf("now running time is %.7f\\n",(float)(end_time - start_time)/CLOCKS_PER_SEC);
#else
#define debug(...)
#define gettime()
#endif
typedef unsigned int uint;
typedef long long int Int;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I_de(x,n)for(int i=0;i<n;i++)printf("%d ",x[i]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp[htx][hty]);}Pln();}
#define M 20
#define PII pair<int,int>
#define PB push_back
#define oo INT_MAX
#define Set_oo 0x3f
#define FOR(it,c) for(vector<PII>::iterator it=(c).begin();it!=(c).end();it++)
#define eps 1e-6
clock_t start_time=clock(), end_time;
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
int min3(int x,int y,int z){
int tmp=min(x,y);
return min(tmp,z);
}
int max3(int x,int y,int z){
int tmp=max(x,y);
return max(tmp,z);
}
int w;
int bw[M];
int killget[1<<17];
Int dp[1<<17];
int n;
void solve(){
Set(dp,0);
Set(killget,0);
killget[0]=w;
for(int i=1;i<(1<<n);i++){
killget[i]=killget[0];
for(int j=0;j<n;j++){
if((i>>j)&1)killget[i]|=bw[j];
}
}
dp[0]=1;
for(int i=1;i<(1<<n);i++){
for(int j=0;j<n;j++){
if(((i>>j)&1)&&((killget[i^(1<<j)]>>j)&1)){
dp[i]+=dp[i^(1<<j)];
}
}
}
printf("%lld\\n",dp[(1<<n)-1]);
}
int main() {
ios_base::sync_with_stdio(0);
char str[20];
int test;
scanf("%d",&test);
int ff=0;
while(test--){
scanf("%d",&n);
scanf("%s",str);
w=0;
Set(bw,0);
for(int i=0;i<n;i++){
if(str[i]-'0')w|=(1<<i);
}
for(int i=0;i<n;i++){
scanf("%s",str);
for(int j=0;j<n;j++){
if(str[j]-'0'){
bw[i]|=(1<<j);
}
}
}
printf("Case %d: ",++ff);
solve();
}
}