Problem Link : http://lightoj.com:81/volume/problem/1055
#include <bits/stdc++.h>
#define pii pair <int,int>
#define pll pair <long long,long long>
#define sc scanf
#define pf printf
#define Pi 2*acos(0.0)
#define ms(a,b) memset(a, b, sizeof(a))
#define pb(a) push_back(a)
#define MP make_pair
#define db double
#define ll long long
#define EPS 10E-10
#define ff first
#define ss second
#define sqr(x) (x)*(x)
#define D(x) cout<<#x " = "<<(x)<<endl
#define VI vector <int>
#define DBG pf("Hi\n")
#define MOD 1000000007
#define CIN ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a) (int)a.size()
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v) for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define RREP(i,a,b) for(int i=a;i>=b;i--)
#define TEST_CASE(t) for(int z=1;z<=t;z++)
#define PRINT_CASE printf("Case %d: ",z)
#define CASE_PRINT cout<<"Case "<<z<<": "
#define all(a) a.begin(),a.end()
#define intlim 2147483648
#define infinity (1<<28)
#define ull unsigned long long
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
using namespace std;
/*----------------------Graph Moves----------------*/
const int fx[]= {+1,-1,+0,+0};
const int fy[]= {+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*------------------------------------------------*/
/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/
struct data
{
pii a,b,c;
};
string graph[15];
map<pii,bool>mp;
int n;
bool vis[10][10][10][10][10][10];
int dis[10][10][10][10][10][10];
bool check(pii aa)
{
if(aa.ff>=0 && aa.ff<n && aa.ss>=0 && aa.ss<n && graph[aa.ff][aa.ss]!='#')
return 1;
return 0;
}
int bfs(data src)
{
vis[src.a.ff][src.a.ss][src.b.ff][src.b.ss][src.c.ff][src.c.ss]=1;
dis[src.a.ff][src.a.ss][src.b.ff][src.b.ss][src.c.ff][src.c.ss]=0;
queue<data>Q;
Q.push(src);
while(!Q.empty())
{
data u=Q.front();
Q.pop();
if(mp[u.a] && mp[u.b] && mp[u.c] && u.a!=u.b && u.a!=u.c && u.b!=u.c)
{
return dis[u.a.ff][u.a.ss][u.b.ff][u.b.ss][u.c.ff][u.c.ss];
}
for(int i=0; i<4; i++)
{
data v;
pii aa=pii(u.a.ff+fx[i],u.a.ss+fy[i]);
if(!check(aa)) aa=u.a;
pii bb=pii(u.b.ff+fx[i],u.b.ss+fy[i]);
if(!check(bb)) bb=u.b;
pii cc=pii(u.c.ff+fx[i],u.c.ss+fy[i]);
if(!check(cc)) cc=u.c;
if(aa==bb)
{
if(bb==cc)
cc=u.c;
aa=u.a;
bb=u.b;
}
if(aa==cc)
{
aa=u.a;
cc=u.c;
}
if(bb==cc)
{
bb=u.b;
cc=u.c;
if(bb==aa)
aa=u.a;
}
v.a=aa;
v.b=bb;
v.c=cc;
if(vis[v.a.ff][v.a.ss][v.b.ff][v.b.ss][v.c.ff][v.c.ss]==0)
{
vis[v.a.ff][v.a.ss][v.b.ff][v.b.ss][v.c.ff][v.c.ss]=1;
dis[v.a.ff][v.a.ss][v.b.ff][v.b.ss][v.c.ff][v.c.ss]=dis[u.a.ff][u.a.ss][u.b.ff][u.b.ss][u.c.ff][u.c.ss]+1;
Q.push(v);
}
}
}
return -1;
}
int main()
{
///freopen("in.txt","r",stdin);
///freopen("out.txt","w",stdout);
CIN;
int t;
cin>>t;
TEST_CASE(t)
{
cin>>n;
loop(i,n) cin>>graph[i];
mp.clear();
data src;
loop(i,n) loop(j,n)
{
if(graph[i][j]=='X') mp[pii(i,j)]=1;
if(graph[i][j]=='A') src.a=pii(i,j);
if(graph[i][j]=='B') src.b=pii(i,j);
if(graph[i][j]=='C') src.c=pii(i,j);
}
ms(vis,0);
ms(dis,0);
int ans=bfs(src);
CASE_PRINT;
if(ans==-1)
cout<<"trapped"<<endl;
else
cout<<ans<<endl;
}
return 0;
}