7764536bd3 2013-11-29        kinaba: #include <iostream>
7764536bd3 2013-11-29        kinaba: #include <sstream>
7764536bd3 2013-11-29        kinaba: #include <iomanip>
7764536bd3 2013-11-29        kinaba: #include <vector>
7764536bd3 2013-11-29        kinaba: #include <string>
7764536bd3 2013-11-29        kinaba: #include <map>
7764536bd3 2013-11-29        kinaba: #include <set>
7764536bd3 2013-11-29        kinaba: #include <algorithm>
7764536bd3 2013-11-29        kinaba: #include <numeric>
7764536bd3 2013-11-29        kinaba: #include <iterator>
7764536bd3 2013-11-29        kinaba: #include <functional>
7764536bd3 2013-11-29        kinaba: #include <complex>
7764536bd3 2013-11-29        kinaba: #include <queue>
7764536bd3 2013-11-29        kinaba: #include <stack>
7764536bd3 2013-11-29        kinaba: #include <cmath>
7764536bd3 2013-11-29        kinaba: #include <cassert>
7764536bd3 2013-11-29        kinaba: #include <tuple>
7764536bd3 2013-11-29        kinaba: using namespace std;
7764536bd3 2013-11-29        kinaba: typedef long long LL;
7764536bd3 2013-11-29        kinaba: typedef complex<double> CMP;
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: LL gcd(LL a, LL b)
7764536bd3 2013-11-29        kinaba: {
7764536bd3 2013-11-29        kinaba: 	while(a)
7764536bd3 2013-11-29        kinaba: 		swap(a, b%=a);
7764536bd3 2013-11-29        kinaba: 	return b;
7764536bd3 2013-11-29        kinaba: }
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: class ConvexPolygonGame { public:
7764536bd3 2013-11-29        kinaba: 	string winner(vector <int> X, vector <int> Y)
7764536bd3 2013-11-29        kinaba: 	{
7764536bd3 2013-11-29        kinaba: 		return has_int_triangle(X, Y) ? "Masha" : "Petya";
7764536bd3 2013-11-29        kinaba: 	}
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 	bool has_int_triangle(const vector<int>& X, const vector<int>& Y)
7764536bd3 2013-11-29        kinaba: 	{
7764536bd3 2013-11-29        kinaba: 		const int xm = *min_element(X.begin(), X.end());
7764536bd3 2013-11-29        kinaba: 		const int xM = *max_element(X.begin(), X.end());
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 		vector< pair<int,int> > p;
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 		int nc = 0, two = 0, dis = 0;
7764536bd3 2013-11-29        kinaba: 		for(int x=xm; x<=xM; ++x)
7764536bd3 2013-11-29        kinaba: 		{
7764536bd3 2013-11-29        kinaba: 			int ym, yM;
7764536bd3 2013-11-29        kinaba: 			tie(ym, yM) = y_range(x, X, Y);
7764536bd3 2013-11-29        kinaba: 			if(ym <= yM) {
7764536bd3 2013-11-29        kinaba: 				dis ++;
7764536bd3 2013-11-29        kinaba: 				nc += (yM - ym + 1);
7764536bd3 2013-11-29        kinaba: 				if(yM-ym+1 >= 2)
7764536bd3 2013-11-29        kinaba: 					two ++;
7764536bd3 2013-11-29        kinaba: 				else
7764536bd3 2013-11-29        kinaba: 					p.emplace_back(x, ym);
7764536bd3 2013-11-29        kinaba: 			}
7764536bd3 2013-11-29        kinaba: //			cerr << nc << "," << two << " : " << x << " " << ym << " ~ " << yM << endl;
7764536bd3 2013-11-29        kinaba: 			if(nc>=3 && two>=1 && dis>=2)
7764536bd3 2013-11-29        kinaba: 				return true;
7764536bd3 2013-11-29        kinaba: 		}
7764536bd3 2013-11-29        kinaba: 		if(nc>=3 && two==0 && dis>=2)
7764536bd3 2013-11-29        kinaba: 		{
7764536bd3 2013-11-29        kinaba: 			double am, aM;
7764536bd3 2013-11-29        kinaba: 			for(int i=1; i<p.size(); ++i)
7764536bd3 2013-11-29        kinaba: 			{
7764536bd3 2013-11-29        kinaba: 				double a = double(p[i].second - p[0].second) / (p[i].first - p[0].first);
7764536bd3 2013-11-29        kinaba: 				if(i==1)am=aM=a;
7764536bd3 2013-11-29        kinaba: 				else am=min(am, a), aM=max(aM,a);
7764536bd3 2013-11-29        kinaba: 			}
7764536bd3 2013-11-29        kinaba: 			return (aM-am) > 1e-9;
7764536bd3 2013-11-29        kinaba: 		}
7764536bd3 2013-11-29        kinaba: 		return false;
7764536bd3 2013-11-29        kinaba: 	}
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 	tuple<int,int> y_range(int x, const vector<int>& X, const vector<int>& Y)
7764536bd3 2013-11-29        kinaba: 	{
7764536bd3 2013-11-29        kinaba: 		vector< pair<LL,LL> > cross;
7764536bd3 2013-11-29        kinaba: 		vector< pair<LL,LL> > exact;
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 		const int N = X.size();
7764536bd3 2013-11-29        kinaba: 		for(int i=0; i<N; ++i)
7764536bd3 2013-11-29        kinaba: 		{
7764536bd3 2013-11-29        kinaba: 			int x1=X[i], x2=X[(i+1)%N];
7764536bd3 2013-11-29        kinaba: 			int y1=Y[i], y2=Y[(i+1)%N];
7764536bd3 2013-11-29        kinaba: 			if(x1 > x2)
7764536bd3 2013-11-29        kinaba: 				swap(x1, x2), swap(y1, y2);
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 			if(x1 == x2)
7764536bd3 2013-11-29        kinaba: 			{
7764536bd3 2013-11-29        kinaba: 				if(x == x1) {
7764536bd3 2013-11-29        kinaba: 					cross.emplace_back(y1,1);
7764536bd3 2013-11-29        kinaba: 					cross.emplace_back(y2,1);
7764536bd3 2013-11-29        kinaba: 					exact.emplace_back(y1,1);
7764536bd3 2013-11-29        kinaba: 					exact.emplace_back(y2,1);
7764536bd3 2013-11-29        kinaba: 				}
7764536bd3 2013-11-29        kinaba: 			}
7764536bd3 2013-11-29        kinaba: 			else
7764536bd3 2013-11-29        kinaba: 			{
7764536bd3 2013-11-29        kinaba: 				if(x<x1 || x2<x)
7764536bd3 2013-11-29        kinaba: 					continue;
7764536bd3 2013-11-29        kinaba: 				LL q = LL(y2-y1)*(x-x1) + LL(y1)*(x2-x1);
7764536bd3 2013-11-29        kinaba: 				LL d = LL(x2-x1);
7764536bd3 2013-11-29        kinaba: 				LL g = gcd(abs(q), d);
7764536bd3 2013-11-29        kinaba: 				cross.emplace_back(q/g, d/g);
7764536bd3 2013-11-29        kinaba: 				if(x==x1 || x==x2)
7764536bd3 2013-11-29        kinaba: 					exact.emplace_back(q/g, d/g);
7764536bd3 2013-11-29        kinaba: 			}
7764536bd3 2013-11-29        kinaba: 		}
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 		sort(cross.begin(), cross.end());
7764536bd3 2013-11-29        kinaba: 		cross.erase(unique(cross.begin(), cross.end()), cross.end());
7764536bd3 2013-11-29        kinaba: 		if(cross.size() == 2) {
7764536bd3 2013-11-29        kinaba: 			LL q1 = cross[0].first;
7764536bd3 2013-11-29        kinaba: 			LL d1 = cross[0].second;
7764536bd3 2013-11-29        kinaba: 			LL q2 = cross[1].first;
7764536bd3 2013-11-29        kinaba: 			LL d2 = cross[1].second;
7764536bd3 2013-11-29        kinaba: 			if(q1*d2 > q2*d1)
7764536bd3 2013-11-29        kinaba: 				swap(q1,q2), swap(d1,d2);
7764536bd3 2013-11-29        kinaba: 			int ym = ceil_div(q1, d1);
7764536bd3 2013-11-29        kinaba: 			int yM = floor_div(q2, d2);
7764536bd3 2013-11-29        kinaba: 			bool ym_exact = false, yM_exact = false;
7764536bd3 2013-11-29        kinaba: 			for(int i=0; i<exact.size(); ++i) {
7764536bd3 2013-11-29        kinaba: 				if(ym*exact[i].second == exact[i].first)
7764536bd3 2013-11-29        kinaba: 					ym_exact = true;
7764536bd3 2013-11-29        kinaba: 				if(yM*exact[i].second == exact[i].first)
7764536bd3 2013-11-29        kinaba: 					yM_exact = true;
7764536bd3 2013-11-29        kinaba: 			}
7764536bd3 2013-11-29        kinaba: 			return make_tuple(ym_exact ? ym+1 : ym, yM_exact ? yM-1 : yM);
7764536bd3 2013-11-29        kinaba: 		}
7764536bd3 2013-11-29        kinaba: 		return make_tuple(-9998, -9999);
7764536bd3 2013-11-29        kinaba: 	}
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 	static int floor_div(LL a, LL b)
7764536bd3 2013-11-29        kinaba: 	{
7764536bd3 2013-11-29        kinaba: 		if(a>=0) return int(a/b);
7764536bd3 2013-11-29        kinaba: 		return int(-((-a+b-1)/b));
7764536bd3 2013-11-29        kinaba: 	}
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: 	static int ceil_div(LL a, LL b)
7764536bd3 2013-11-29        kinaba: 	{
7764536bd3 2013-11-29        kinaba: 		if(a>=0) return int((a+b-1)/b);
7764536bd3 2013-11-29        kinaba: 		return int(-((-a)/b));
7764536bd3 2013-11-29        kinaba: 	}
7764536bd3 2013-11-29        kinaba: };
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: // BEGIN CUT HERE
7764536bd3 2013-11-29        kinaba: #include <ctime>
7764536bd3 2013-11-29        kinaba: double start_time; string timer()
7764536bd3 2013-11-29        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
7764536bd3 2013-11-29        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
7764536bd3 2013-11-29        kinaba:  { os << "{ ";
7764536bd3 2013-11-29        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
7764536bd3 2013-11-29        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
7764536bd3 2013-11-29        kinaba: void verify_case(const string& Expected, const string& Received) {
7764536bd3 2013-11-29        kinaba:  bool ok = (Expected == Received);
7764536bd3 2013-11-29        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
7764536bd3 2013-11-29        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
7764536bd3 2013-11-29        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
7764536bd3 2013-11-29        kinaba: #define END	 verify_case(_, ConvexPolygonGame().winner(X, Y));}
7764536bd3 2013-11-29        kinaba: int main(){
7764536bd3 2013-11-29        kinaba: 
7764536bd3 2013-11-29        kinaba: CASE(0)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 1, 0};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, 0, 1};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Petya";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(1)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 4, 2};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, 0, 2};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Masha";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(2)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 100, 100, 0};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, 0, 100, 100};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Masha";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(3)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 50, 100, 50};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, -1, 0, 1};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Petya";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(4)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {-100000, 100000, 100000, -100000};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {-1, -1, 1, 1};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Masha";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(5)
7764536bd3 2013-11-29        kinaba: 	// 1 1 1 (yoko)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 3, 5, 3};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, 0, 1, 1};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Masha";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(5)
7764536bd3 2013-11-29        kinaba: 	// 1 1 1 (tate)
7764536bd3 2013-11-29        kinaba: 	int X_[] = {0, 1, 1, 0};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba: 	int Y_[] = {0, 3, 5, 3};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Masha";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: CASE(6)
7764536bd3 2013-11-29        kinaba: 	// 3 (tate)  // yoko ha sample
7764536bd3 2013-11-29        kinaba: 	int X_[] = {-1, 0, 1, 0};
7764536bd3 2013-11-29        kinaba: 	  vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
7764536bd3 2013-11-29        kinaba:     int Y_[] = {0, -2, 0, 2};
7764536bd3 2013-11-29        kinaba: 	  vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
7764536bd3 2013-11-29        kinaba: 	string _ = "Petya";
7764536bd3 2013-11-29        kinaba: END
7764536bd3 2013-11-29        kinaba: }
7764536bd3 2013-11-29        kinaba: // END CUT HERE