Problem: You are the God of Wind.

By moving a big cloud around, you can decide the weather: it invariably rains under the cloud, and the sun shines everywhere else.

But you are a benign God: your goal is to give enough rain to every field in the countryside, and sun to markets and festivals. Small humans, in their poor vocabulary, only describe this as “weather forecast”.

You are in charge of a small country, called Paccimc. This country is constituted of 4 × 4 square areas, denoted by their numbers.

<image>

Your cloud is of size 2 × 2, and may not cross the borders of the country.

You are given the schedule of markets and festivals in each area for a period of time.

On the first day of the period, it is raining in the central areas (6-7-10-11), independently of the schedule.

On each of the following days, you may move your cloud by 1 or 2 squares in one of the four cardinal directions (North, West, South, and East), or leave it in the same position. Diagonal moves are not allowed. All moves occur at the beginning of the day.

You should not leave an area without rain for a full week (that is, you are allowed at most 6 consecutive days without rain). You don’t have to care about rain on days outside the period you were given: i.e. you can assume it rains on the whole country the day before the period, and the day after it finishes.



Input

The input is a sequence of data sets, followed by a terminating line containing only a zero.

A data set gives the number N of days (no more than 365) in the period on a single line, followed by N lines giving the schedule for markets and festivals. The i-th line gives the schedule for the i-th day. It is composed of 16 numbers, either 0 or 1, 0 standing for a normal day, and 1 a market or festival day. The numbers are separated by one or more spaces.

Output

The answer is a 0 or 1 on a single line for each data set, 1 if you can satisfy everybody, 0 if there is no way to do it.

Example

Input

1
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1
0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0
7
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0
0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0
0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0
0


Output

0
1
0
1

Solution (in JAVA):

Solution:
import java.util.*;
import static java.lang.Math.*;

public class Main {
	final Scanner sc=new Scanner(System.in);
	public static void main(String[] args) {
		new Main().init();
	}
	void init(){
		//long start=System.currentTimeMillis();
		new AOJ1243DFS();
		//System.out.println(" ["+ (System.currentTimeMillis()-start) +"msec]");
	}
	
	// Asia 2003JP#D Weather forecast(DFS)
	class AOJ1243DFS{
		final int[] v={0,-8,-4,1,2,4,8,-1,-2};
		ArrayList<HashSet<String>> visited;
		AOJ1243DFS(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.println(solve(N)?1:0);
			}
		}
		boolean solve(int N){
			boolean[][] s=new boolean[17][N+1];
			visited=new ArrayList<HashSet<String>>();
			visited.add(new HashSet<String>());
			for(int y=1; y<=N; y++){
				visited.add(new HashSet<String>());
				for(int x=1; x<=16; x++)s[x][y]=(sc.nextInt()==1);
			}
			if(s[6][1] || s[7][1] || s[10][1] || s[11][1])	return false;
			return DFS(6,2,N,"11116",s);
		}
		boolean DFS(int cx,int depth,int N,String r,boolean[][] s){
			if(depth>N)	return true;
			for(int i=0; i<9; i++){
				if(!(cx==1||cx==5||cx==9) && v[i]==2)continue;
				if(!(cx==3||cx==7||cx==11) && v[i]==-2)continue;
				int c=cx+v[i];
				if(!((1<=c && c<=3)||(5<=c && c<=7)||(9<=c && c<=11)))	continue;
				if(s[c][depth] || s[c+1][depth] || s[c+4][depth] || s[c+5][depth])	continue;
				int[] r2=decode(r);
				switch(c){
				case 1:r2[0]=-1;	break;
				case 3:r2[1]=-1;	break;
				case 11:r2[2]=-1;	break;
				case 9:r2[3]=-1;	break;
				}
				boolean f=true;
				for(int j=0; j<4; j++)if(++r2[j]>6)f=false;
				if(!f)continue;
				String r3=encode(r2,c);
				if(visited.get(depth).contains(r3))continue;
				visited.get(depth).add(r3);
				if(DFS(c,depth+1,N,r3,s))	return true;
			}
			return false;
		}
		int[] decode(String r){
			int[] ret=new int[4];
			for(int i=0; i<4; i++)ret[i]=r.charAt(i)-'0';
			return ret;
		}
		String encode(int[] r,int c){
			StringBuilder ret=new StringBuilder();
			for(int i=0; i<4; i++)ret.append(r[i]);
			ret.append(c);
			return ret.toString();
		}
	}
	
	
	// Asia 2003JP#D Weather forecast(BFS)
	class AOJ1243BFS{
		final int[] v={0,-8,-4,1,2,4,8,-1,-2};
		AOJ1243BFS(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.println(solve(N)?1:0);
			}
		}
		boolean solve(int N){
			boolean[][] s=new boolean[17][N+1];
			ArrayList<HashSet<String>> closed=new ArrayList<HashSet<String>>();
			for(int y=1; y<=N; y++){
				closed.add(new HashSet<String>());
				for(int x=1; x<=16; x++)s[x][y]=(sc.nextInt()==1);
			}
			if(s[6][1] || s[7][1] || s[10][1] || s[11][1])	return false;
			LinkedList<State> open=new LinkedList<Main.AOJ1243BFS.State>();
			open.add(new State(2, 6, "11116"));
			while(!open.isEmpty()){
				State now=open.poll();
				if(now.day>N)	return true;
				for(int i=0; i<9; i++){
					if(!(now.c==1||now.c==5||now.c==9) && v[i]==2)continue;
					if(!(now.c==3||now.c==7||now.c==11) && v[i]==-2)continue;
					int cc=now.c+v[i];
					if(!((1<=cc && cc<=3)||(5<=cc && cc<=7)||(9<=cc && cc<=11)))	continue;
					if(s[cc][now.day] || s[cc+1][now.day] || s[cc+4][now.day] || s[cc+5][now.day])	continue;
					int[] r=now.decode();
					switch(cc){
					case 1:r[0]=-1;		break;
					case 3:r[1]=-1;		break;
					case 11:r[2]=-1;	break;
					case 9:r[3]=-1;		break;
					}
					boolean f=true;
					for(int j=0; j<4; j++)if(++r[j]>6)f=false;
					if(!f)continue;
					State next=new State(now.day+1, cc, r);
					if(next.day>N)	return true;
					if(closed.get(now.day).contains(next.r))continue;
					open.add(next);
					closed.get(now.day).add(next.r);
				}
			}
			return false;
		}
		class State{
			int c,day;
			String r;
			State(int day,int c,String r){
				this.day=day;
				this.c=c;
				this.r=r;
			}
			State(int day,int c,int[] r){
				this.day=day;
				this.c=c;
				StringBuilder tmp=new StringBuilder();
				for(int i=0; i<4; i++)tmp.append(r[i]);
				tmp.append(c);
				this.r=tmp.toString();
			}
			int[] decode(){
				int[] ret=new int[4];
				for(int i=0; i<4; i++)ret[i]=r.charAt(i)-'0';
				return ret;
			}
		}
	}
	
	
	// Confusing Login Names
	class AOJ1252{
		AOJ1252(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				solve(N);
			}
		}
		void solve(int N){
			int D=sc.nextInt();
			String[] names=new String[N];
			for(int i=0; i<N; i++)	names[i]=sc.next();
			Arrays.sort(names);
			ArrayList<TreeSet<String>> state1=new ArrayList<TreeSet<String>>(),state2=new ArrayList<TreeSet<String>>();
			//ArrayList<HashSet<String>> state1=new ArrayList<HashSet<String>>(),state2=new ArrayList<HashSet<String>>();
			for(int i=0; i<N; i++){
				TreeSet<String> tmp=new TreeSet<String>();
				//HashSet<String> tmp=new HashSet<String>();
				for(int j=0; j<names[i].length(); j++){
					tmp.add(new StringBuilder(names[i]).deleteCharAt(j).toString());
					for(int k=0; k<26; k++){
						char c=(char)('a'+k);
						tmp.add(new StringBuilder(names[i]).insert(j, c).toString());
						StringBuilder sb=new StringBuilder(names[i]);
						sb.setCharAt(j, c);
						tmp.add(sb.toString());
					}
					tmp.add(swap(j,min(j+1,names[i].length()-1),names[i]));
				}
				for(int k=0; k<26; k++)	tmp.add(names[i]+(char)('a'+k));
				state1.add(tmp);
			}
			if(D>1)	state2=state1;
			else{
				for(int i=0; i<N; i++){
					TreeSet<String> tmp=new TreeSet<String>();
					//HashSet<String> tmp=new HashSet<String>();
					tmp.add(names[i]);
					state2.add(tmp);
				}
			}
			
			TreeSet<Pair> ans=new TreeSet<Main.AOJ1252.Pair>();
			for(int i=0; i<N; i++){
				for(int j=i+1; j<N; j++){
					if(names[i].length()-names[j].length()>4)	continue;
					for(String s:state1.get(i)){
						if(state2.get(j).contains(s))	ans.add(new Pair(names[i],names[j]));
					}
				}
			}
			for(Pair p:ans)	System.out.println(p);
			System.out.println(ans.size());
		}
		String swap(int a,int b,String str){
			StringBuilder sb=new StringBuilder(str);
			char tmp=sb.charAt(a);
			sb.setCharAt(a, sb.charAt(b));
			sb.setCharAt(b, tmp);
			return sb.toString();
		}
		class Pair implements Comparable<Pair>{
			String s1,s2;
			Pair(String s1,String s2){
				this.s1=s1;
				this.s2=s2;
			}
			@Override public int compareTo(Pair p){
				if(s1==p.s2 && s2==p.s1)	return 0;
				return s1.compareTo(p.s1)!=0?s1.compareTo(p.s1) :s2.compareTo(p.s2);
			}
			@Override public String toString(){
				return s1+","+s2;
			}
		}
	}
	
	
	// Gap
	class AOJ1245{
		AOJ1245(){
			int N=sc.nextInt();
			while(--N>=0)	solve();
		}
		void solve(){
			StringBuilder init=new StringBuilder(),fin=new StringBuilder();
			for(int i=1; i<=4; i++){
				init.append("##");
				for(int j=1; j<=7; j++){
					init.append(sc.nextInt());
					fin.append(i);	fin.append(j);
				}
				fin.append("##");
			}
			for(int i=0; i<32; i++){
				if(init.charAt(i*2+1)=='1')	nSwap(i*2,(init.charAt(i*2)-'0'-1)*16,init);
			}
			int ans=-1;
			PriorityQueue<State1> open=new PriorityQueue<State1>();
			open.add(new State1(init,0));
			HashMap<String,Integer> closed=new HashMap<String, Integer>();
			closed.put(init.toString(),0);
			while(!open.isEmpty()){
				State1 now=open.poll();
				if(now.sb.toString().equals(fin.toString())){
					ans=now.step;
					break;
				}
				for(int i=0; i<32; i++){
					if(now.sb.charAt(i*2)=='#' && now.sb.charAt((i-1)*2)!='#'){
						int s=now.sb.charAt((i-1)*2)-'0',v=now.sb.charAt((i-1)*2+1)-'0';
						if(v>=7)	continue;
						boolean bf=false;
						for(int j=0; j<32; j++){
							if(now.sb.charAt(j*2)-'0'==s && now.sb.charAt(j*2+1)-'0'==v+1){
								StringBuilder tmp=new StringBuilder(now.sb);
								nSwap(i*2,j*2,tmp);
								if(tmp.toString().equals(fin.toString())){
									ans=now.step+1;
									open.clear();
									bf=true;
									break;
								}
								if(closed.containsKey(tmp.toString()) && closed.get(tmp.toString())<=now.step+1)	break;
								open.add(new State1(tmp,now.step+1));
								closed.put(tmp.toString(),now.step+1);
								break;
							}
						}
						if(bf)	break;
					}
				}
			}
			System.out.println(ans);
		}
		void nSwap(int a,int b,StringBuilder sb){
			if(a==b)	return;
			swap(a,b,sb);
			swap(++a,++b,sb);
		}
		void swap(int a,int b,StringBuilder sb){
			char tmp=sb.charAt(a);
			sb.setCharAt(a, sb.charAt(b));
			sb.setCharAt(b, tmp);
		}
		class State1 implements Comparable<State1>{
			StringBuilder sb;
			int step;
			State1(StringBuilder sb,int step){
				this.sb=sb;	this.step=step;
			}
			@Override public int compareTo(State1 o) {
				return this.step-o.step;
			}
		}
	}
	
	class AOJ1258{
		final int INF=Integer.MAX_VALUE/4;
		AOJ1258(){
			while(true){
				int M=sc.nextInt(),C=sc.nextInt(),N=sc.nextInt();
				if(((M|C)|N)==0)	break;
				System.out.println(solve(M,C,N));
			}
		}
		int solve(int M,int C,int N){
			LinkedList<LinkedList<Integer>> q=new LinkedList<LinkedList<Integer>>();
			for(int i=0; i<N; i++){
				q.add(new LinkedList<Integer>());
				int K=sc.nextInt();
				for(int j=0; j<K; j++)	q.getLast().add(sc.nextInt());
			}
			Store store=new Store(M,C);
			int ans=0;
			while(!q.isEmpty()){
				int r=q.getFirst().poll();
				ans+=store.take(r);
				ans+=store.put(r);
				//debug
				//System.out.println(store);
				if(q.getFirst().isEmpty())	q.removeFirst();
				else	q.addLast(q.poll());
			}
			return ans;
		}
		class Store{
			int M,C,time;
			ArrayList<ArrayList<Book>> desks;
			Store(int m,int c){
				this.M=m;	this.C=c;	this.time=0;
				desks=new ArrayList<ArrayList<Book>>();
				for(int i=0; i<M; i++)	desks.add(new ArrayList<Book>());
			}
			int take(int r){
				int ret=M+1;
				for(int i=0; i<M; i++){
					for(int j=0; j<desks.get(i).size(); j++){
						if(desks.get(i).get(j).id==r){
							desks.get(i).remove(j);
							ret=i+1;
							break;
						}
					}
					if(ret<M+1)	break;
				}
				return ret;
			}
			int put(int r){
				int ret=M+1;
				if(desks.get(0).size()<C){
					desks.get(0).add(new Book(r,time++));
					ret=1;
				}else{
					ret=0;
					Pair tmpIdx=new Pair(M,0);
					for(int i=1; i<M; i++){
						if(desks.get(i).size()<C){
							tmpIdx.first=i;
							desks.get(i).add(new Book(INF,INF));
							tmpIdx.second=desks.get(i).size()-1;
							break;
						}
					}
					ret+=tmpIdx.first+1;
					int oldestTime=desks.get(0).get(0).t,oldestIdx=0;
					for(int i=1; i<desks.get(0).size(); i++){
						if(oldestTime>desks.get(0).get(i).t){
							oldestTime=desks.get(0).get(i).t;
							oldestIdx=i;
						}
					}
					Book oldest=desks.get(0).remove(oldestIdx);
					ret+=1;
					int empIdx=M;
					for(int i=1; i<M; i++){
						if(desks.get(i).size()<C){
							desks.get(i).add(oldest);
							empIdx=i;
							break;
						}
					}
					ret+=empIdx+1;
					if(tmpIdx.first<M)	desks.get(tmpIdx.first).remove(tmpIdx.second);
					ret+=tmpIdx.first+1;
					desks.get(0).add(new Book(r,time++));
					ret+=1;
				}
				return ret;
			}
			@Override public String toString(){return desks.toString();}
		}
		class Book{
			int id,t;
			Book(int id,int t){this.id=id;this.t=t;}
			@Override public String toString(){return "ID"+id+" T"+t;}
		}
		class Pair implements Comparable<Pair>{
			int first,second;
			Pair(int first,int second){this.first=first; this.second=second;}
			@Override public String toString(){return "("+first+","+second+")";}
			@Override public int compareTo(Pair p){
				if(this.first<p.first)	return -1;
				if(this.first>p.first)	return 1;
				if(this.second<p.second)	return -1;
				if(this.second>p.second)	return 1;
				return 0;
			}
			@Override public int hashCode(){
				return 17+31*first+second;
			}
			@Override public boolean equals(Object obj){
				if(this==obj)	return true;
				if(obj==null)	return false;
				if(this.getClass() != obj.getClass())	return false;
				Pair p=(Pair)obj;
				if(this.first==p.first&&this.second==p.second)	return true;
				return false;
			}
		}
	}
	
	class AOJ1262{
		final double INF=Double.MAX_VALUE/4.0;
		AOJ1262(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.printf("%.4f\n",solve(N));
			}
		}
		double solve(int N){
			int[] a=new int[N+1];
			for(int i=1; i<=N; i++)	a[i]=sc.nextInt();
			double b=sc.nextDouble();
			int r=sc.nextInt();
			double v=sc.nextDouble(),e=sc.nextDouble(),f=sc.nextDouble();
			double[][] dp=new double[N+1][N+1];
			for(int i=1; i<=N; i++)for(int j=0; j<=N; j++)dp[i][j]=INF;
			//flash(dp,N);
			double tmp=0.0;
			for(int i=0; i<a[1]; i++)	tmp+=exp(i,r,v,e,f);
			dp[1][0]=tmp;
			for(int w=1; w<N; w++){
				for(int h=0; h<w; h++){
					int d=a[w+1]-a[w],x=a[w]-a[h];
					double exp=0.0;
					for(int i=0; i<d; i++)	exp+=exp(x++,r,v,e,f);
					//debug
					//System.out.println(exp);
					dp[w+1][h]=dp[w][h]+exp;
					double exp2=0.0;
					for(int i=0; i<d; i++)	exp2+=exp(i,r,v,e,f);
					dp[w+1][w]=min(dp[w+1][w], dp[w][h]+exp2+b);
				}
				//debug
				//System.out.println("new "+dp[w+1][w]);
			}
			//flash(dp,N);
			double ans=INF;
			for(int i=0; i<=N; i++)	ans=min(ans,dp[N][i]);
			return ans;
		}
		double exp(int x,double r,double v,double e,double f){
			return x>=r?(1/(v-e*(x-r))):(1/(v-f*(r-x)));
		}
		void flash(double[][] dp,int N){
			for(int y=0; y<=N; y++){
				for(int x=0; x<=N; x++)	System.out.printf("%3.3f ",dp[x][y]>=INF?-1:dp[x][y]);
				System.out.println();
			}
		}
	}
}