#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;
class EllysBulls { public:
string getNumber(vector <string> guesses, vector <int> bulls)
{
vector<int> pTen(1,1);
for(int i=0; i<10; ++i)
pTen.push_back(pTen.back()*10);
int Q = guesses.size();
int N = guesses[0].size();
int B = min(N, 4);
int F = N - B;
map<string, vector<int> > back;
for(int b=0; b<pTen[B]; ++b)
{
string sig;
for(int i=0; i<Q; ++i)
{
int s = bulls[i];
for(int k=0; k<B; ++k)
if( (guesses[i][N-1-k]-'0') == b/pTen[k]%10 )
--s;
if(s>=0)
sig += char('0'+s);
else
goto next;
}
back[sig].push_back(b);
next:;
}
string cand = "";
for(int f=0; f<pTen[F]; ++f)
{
string sig;
map<string, vector<int> >::iterator it;
for(int i=0; i<Q; ++i)
{
int s = 0;
for(int k=0; k<F; ++k)
if( (guesses[i][F-1-k]-'0') == f/pTen[k]%10 )
++s;
if(s<=bulls[i])
sig += char('0'+s);
else
goto next2;
}
it = back.find(sig);
if( it != back.end() ) {
for(int j=0; j<it->second.size(); ++j) {
if(!cand.empty())
return "Ambiguity";
for(int k=0; k<F; ++k)
cand += char('0'+f/pTen[F-1-k]%10);
for(int k=0; k<B; ++k)
cand += char('0'+it->second[j]/pTen[B-1-k]%10);
}
}
next2:;
}
if(cand.empty())
return "Liar";
return cand;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const string& Expected, const string& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, EllysBulls().getNumber(guesses, bulls));}
int main(){
CASE(0)
string guesses_[] = {"1234", "4321", "1111", "2222", "3333", "4444", "5555", "6666", "7777", "8888", "9999"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {2, 1, 1, 0, 2, 0, 0, 0, 1, 0, 0};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "1337";
END
CASE(1)
string guesses_[] = {"0000", "1111", "2222"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {2, 2, 2};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "Liar";
END
CASE(2)
string guesses_[] = {"666666", "666677", "777777", "999999"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {2, 3, 1, 0};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "Ambiguity";
END
CASE(3)
string guesses_[] = {"000", "987", "654", "321", "100", "010"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {2, 1, 0, 0, 1, 1};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "007";
END
CASE(4)
string guesses_[] = {"28", "92", "70", "30", "67", "63", "06", "65",
"11", "06", "88", "48", "09", "65", "48", "08"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "54";
END
CASE(5)
string guesses_[] = {"0294884", "1711527", "2362216", "7666148", "7295642",
"4166623", "1166638", "2767693", "8650248", "2486509",
"6138934", "4018642", "6236742", "2961643", "8407361",
"2097376", "6575410", "6071777", "3569948", "2606380"};
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = {1, 0, 1, 3, 4, 4, 3, 2, 1, 1, 0, 4, 4, 3, 0, 0, 0, 0, 2, 1};
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = "4266642";
END
/*
CASE(6)
string guesses_[] = ;
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = ;
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = ;
END
CASE(7)
string guesses_[] = ;
vector <string> guesses(guesses_, guesses_+sizeof(guesses_)/sizeof(*guesses_));
int bulls_[] = ;
vector <int> bulls(bulls_, bulls_+sizeof(bulls_)/sizeof(*bulls_));
string _ = ;
END
*/
}
// END CUT HERE