#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>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;

class ChickenOracle { public:
	string theTruth(int n, int eggCount, int lieCount, int liarCount) 
	{
		bool egg = canTruthTellerBe(   eggCount, n, lieCount, liarCount );
		bool chk = canTruthTellerBe( n-eggCount, n, lieCount, liarCount );
		if( egg && chk ) return "Ambiguous";
		if( egg ) return "The egg";
		if( chk ) return "The chicken";
		return "The oracle is a lie";
	}
	bool canTruthTellerBe( int A, int n, int B, int  C )
	{
		int two_x = A+B+C - n;
		if( (two_x&1) == 1 )
			return false;
		int x = two_x/2;
		return 0<=x && x<=C && x<=B && (C-x)<=(n-B);
	}
};

// 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(_, ChickenOracle().theTruth(n, eggCount, lieCount, liarCount));}
int main(){

CASE(0)
	int n = 10; 
	int eggCount = 10; 
	int lieCount = 0; 
	int liarCount = 0; 
	string _ = "The egg"; 
END
CASE(1)
	int n = 60; 
	int eggCount = 40; 
	int lieCount = 0; 
	int liarCount = 30; 
	string _ = "The oracle is a lie"; 
END
CASE(2)
	int n = 60; 
	int eggCount = 20; 
	int lieCount = 5; 
	int liarCount = 25; 
	string _ = "The chicken"; 
END
CASE(3)
	int n = 1000; 
	int eggCount = 500; 
	int lieCount = 250; 
	int liarCount = 250; 
	string _ = "Ambiguous"; 
END
CASE(4)
	int n = 338919; 
	int eggCount = 310645; 
	int lieCount = 70422; 
	int liarCount = 304279; 
	string _ = "The oracle is a lie"; 
END
CASE(5)
	int n = 1; 
	int eggCount = 0; 
	int lieCount = 0; 
	int liarCount = 0; 
	string _ = "The chicken"; 
END
}
// END CUT HERE
