SPFA finds the shortest path for all English letters, along with all methods.
Remember that the English letters that have been visited can be visited again.
//
// 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 12
#define PII pair<int,int\>
#define PB push\_back
#define oo INT\_MAX
#define Set\_oo 0x3f
#define X first;
#define Y second;
#define FOR(it,c) for(\_\_typeof((c).begin()) 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);
}
char mz\[M\]\[M\];
int kx\[30\],ky\[30\];
int n;
int path\[30\]\[30\];
int meth\[30\]\[30\];
int dx\[\]={0,0,1,-1};
int dy\[\]={1,-1,0,0};
int h;
int mod=20437;
void spfa(char a,char b){
a-='A';
b-='A';
path\[a\]\[b\]=oo;
int bx=kx\[a\];
int by=ky\[a\];
int ex=kx\[b\];
int ey=ky\[b\];
// debug("%d %d %d %d\\n",bx,by,ex,ey);
int dis\[M\]\[M\];
fill(&dis\[0\]\[0\],&dis\[M-1\]\[M-1\],oo);
dis\[bx\]\[by\]=0;
queue<PII> q;
q.push(PII(bx,by));
while(!q.empty()){
int x=q.front().X;
int y=q.front().Y;
// debug("%d %d\\n",x,y);
// debug("%c %c %d\\n",a+'A',b+'A',meth\[a\]\[b\]);
q.pop();
if(x==ex&&y==ey&&dis\[x\]\[y\]<=path\[a\]\[b\]){
path\[a\]\[b\]=dis\[x\]\[y\];
meth\[a\]\[b\]++;
continue;
}
for(int i=0;i<4;i++){
int nx=x+dx\[i\],ny=y+dy\[i\];
if(nx<0||nx>=n||ny<0||ny>=n)continue;
if(mz\[ny\]\[nx\]=='#')continue;
if(isalpha(mz\[ny\]\[nx\])&&mz\[ny\]\[nx\]>b+'A')continue;
if(dis\[nx\]\[ny\]>=dis\[x\]\[y\]+1){
dis\[nx\]\[ny\]=dis\[x\]\[y\]+1;
q.push(PII(nx,ny));
}
}
}
if(path\[a\]\[b\]==oo)path\[a\]\[b\]=-1;
}
void solve(){
Set(meth,0);
int ansdis=0,ansmeth=1;
int i;
for(i=1;i<h;i++){
spfa('A'+i-1,'A'+i);
if(path\[i-1\]\[i\]==-1)break;
ansdis=(ansdis+path\[i-1\]\[i\])%mod;
ansmeth=ansmeth\*(meth\[i-1\]\[i\]%mod);
ansmeth%=mod;
}
if(i==h){
printf("%d %d\\n",ansdis,ansmeth);
}else puts("Impossible");
}
int main() {
ios\_base::sync\_with\_stdio(0);
int ff=0;
while(~scanf("%d",&n)&&n){
h=0;
for(int i=0;i<n;i++){
scanf("%s",mz\[i\]);
for(int j=0;j<n;j++){
if(isalpha(mz\[i\]\[j\])){
kx\[mz\[i\]\[j\]-'A'\]=j;
ky\[mz\[i\]\[j\]-'A'\]=i;
h++;
}
}
}
printf("Case %d: ",++ff);
solve();
}
}