User ainta has a permutation p1, p2, ..., pn. As the New Year is coming, he wants to make his permutation as pretty as possible.

Permutation a1, a2, ..., an is prettier than permutation b1, b2, ..., bn, if and only if there exists an integer k (1 ≤ k ≤ n) where a1 = b1, a2 = b2, ..., ak - 1 = bk - 1 and ak < bk all holds.

As known, permutation p is so sensitive that it could be only modified by swapping two distinct elements. But swapping two elements is harder than you think. Given an n × n binary matrix A, user ainta can swap the values of pi and pj (1 ≤ i, j ≤ n, i ≠ j) if and only if Ai, j = 1.

Given the permutation p and the matrix A, user ainta wants to know the prettiest permutation that he can obtain.

Input

The first line contains an integer n (1 ≤ n ≤ 300) — the size of the permutation p.

The second line contains n space-separated integers p1, p2, ..., pn — the permutation p that user ainta has. Each integer between 1 and n occurs exactly once in the given permutation.

Next n lines describe the matrix A. The i-th line contains n characters '0' or '1' and describes the i-th row of A. The j-th character of the i-th line Ai, j is the element on the intersection of the i-th row and the j-th column of A. It is guaranteed that, for all integers i, j where 1 ≤ i < j ≤ n, Ai, j = Aj, i holds. Also, for all integers i where 1 ≤ i ≤ n, Ai, i = 0 holds.

Output

In the first and only line, print n space-separated integers, describing the prettiest permutation that can be obtained.

Examples

Input

7
5 2 4 3 6 7 1
0001001
0000000
0000010
1000001
0000000
0010000
1001000


Output

1 2 4 3 6 7 5


Input

5
4 2 1 5 3
00100
00011
10010
01101
01010


Output

1 2 3 4 5

Note

In the first sample, the swap needed to obtain the prettiest permutation is: (p1, p7).

In the second sample, the swaps needed to obtain the prettiest permutation is (p1, p3), (p4, p5), (p3, p4). 

<image>

A permutation p is a sequence of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. The i-th element of the permutation p is denoted as pi. The size of the permutation p is denoted as n.
///package DFS;
import java.io.*;
import java.util.*;
/**
 *
 * @author prabhat
 */
public class P500B {


    
	   static final int MAX1 = 1000000+10;
	   static final int MAX2 = 1000001;
	   static final long MOD = 1000000007;
	   static int phiSum[] = new int[MAX1];
	   static int phi[] = new int[MAX1];
	   static long[] res=new long[MAX1];
	   static int p[];
	   static long BIT[];
	   static int k,n;
	   static boolean[] b;
	   static int[][] pascal;
           static long[][] dp;
          public static int[] t;
          static long ans;
          static int[] seq;
          static boolean[] visit;
          static boolean[][]   adj;
	    public static void main(String[] args) throws IOException{
	       
	        InputReader in = new InputReader(System.in);
              // BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	        PrintWriter pw = new PrintWriter(System.out,true);
               n=in.ii();
              p=new int[n];
              seq=new int[n];
              adj=new boolean[n][n];
              visit=new boolean[n];
              for(int i=0;i<n;i++)p[i]=in.ii()-1;
              for(int i=0;i<n;i++)
              {
                String s=in.next().trim();
                for(int j=0;j<n;j++)
                {
                  if(s.charAt(j)=='1')
                      adj[i][j]=true;
                }
              
              }
              int[] val=new int[n];
              for(int i=0;i<n;i++)
              {
                if(visit[i])continue;
                k=0;
                dfs(i);
                Arrays.sort(seq,0,k);
                for(int j=0;j<k;j++) val[j]=p[seq[j]];
                Arrays.sort(val,0,k);
               for(int j=0;j<k;j++)p[seq[j]]=val[j];
              
              }
              for(int i=0;i<n;i++)
                  pw.print(p[i]+1+" ");
              
	       pw.close();
	    }
            static void dfs(int cur)
            {
              if(visit[cur])return ;
              visit[cur]=true;
              seq[k++]=cur;
              for(int i=0;i<n;i++)
                  if(adj[cur][i])
                      dfs(i);
              
            }
   
      static boolean nextPermutation(int[] p) {
        for (int a = p.length - 2; a >= 0; --a)
        {
            if (p[a] < p[a + 1])
                for (int b = p.length - 1; ; --b)
                    if (p[b] > p[a]) {
                        int t = p[a];
                        p[a] = p[b];
                        p[b] = t;
                        for (++a, b = p.length - 1; a < b; ++a, --b) 
                        {
                            t = p[a];
                            p[a] = p[b];
                            p[b] = t;
                        }
                        return true;
                    }
        }
        return false;
     }

	    public static long nCr(long total, long choose)
		{
			if(total < choose)
				return 0;
			if(choose == 0 || choose == total)
				return 1;
			return nCr(total-1,choose-1)+nCr(total-1,choose);
		}
	    static void compute() {
	    		for (int i = 0; i < MAX1; i++) {
	    			phi[i] = 0;
	    		}
	          phi[1]=1;
	    		for (int i = 2; i < MAX1; i++) {
	    			if (phi[i] == 0) {
	    				phi[i] = i - 1;
	     
	    				for (int j = 2 * i; j < MAX1; j += i) {
	    					 if(phi[j]==0) phi[j] = j ;
	    					phi[j] -= (phi[j]/i);
	    				}
	    			}
	    		}
	     
	    		for (int i = 1; i < MAX1; i++) {
	    			for (int j = i, k = 1; j < MAX1; j += i,k++) {
	    				phiSum[j] += i * phi[k];
	    			}
	    		}
	    		//System.out.println(Arrays.toString(phiSum));
                /*botharrays  res and phisum gives the same arrays so please don't worry*/
	    		
	    		for(int i=1;i<MAX1;i++)
	    		{
	    			for(int j=i+i;j<MAX1;j+=i)
	    			{
	    			   res[j]=res[j]+1L*i*phi[j/i];
	    			}
	    		}
	    		for(int i=1;i<=1000000;i++)
	    			res[i]=res[i]+res[i-1];
	    	//System.out.println(Arrays.toString(res));
	    						
	    		
	    		
	    }
            public static int[] radixSort(int[] f){ return radixSort(f, f.length); }
	public static int[] radixSort(int[] f, int n)
	{
		int[] to = new int[n];
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(f[i]&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[f[i]&0xffff]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(f[i]>>>16)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[f[i]>>>16]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		return f;
	}
	    public static void Seive()
		{
			
			 b=new boolean[10000001];
			Arrays.fill(b, true);
			b[0]=false;
			b[1]=false;
			
			for(int i=2;i<=(10000000);i++)
			{
				if(b[i])
				{
					
				 for(int j=i*2;j<=10000000;j+=i)
					{
						     b[j]=false;
						
					}
				}
				
			}
			
		}
	    static int pascal(int i1,int j1)
	    {
	  	  pascal=new int[101][101];
	  	  for(int i=0;i<=100;i++)
	  	  {
	  		  pascal[i][0]=1;
	  		  for(int j=1;j<=i;j++)
	  		  {
	  			  pascal[i][j]=(int) ((pascal[i-1][j]+pascal[i-1][j-1])%MOD);
	  		  }
	  	  }
	  	  return pascal[i1][j1];
	    }
	    private static class DSU{
			int[] parent;
			int[] rank;
			int cnt;
			public DSU(int n){
				parent=new int[n];
				rank=new int[n];
				for(int i=0;i<n;i++){
					parent[i]=i;
					rank[i]=1;
				}
				cnt=n;
			}
			int find(int i){
		        while(parent[i] !=i){
		        	parent[i]=parent[parent[i]];
		        	i=parent[i];
		        }
		        return i;
		    }
			int Union(int x, int y){
		        int xset = find(x);
		        int yset = find(y);
		        if(xset!=yset)
		        	cnt--;
		        if(rank[xset]<rank[yset]){
		        	parent[xset] = yset;
			        rank[yset]+=rank[xset];
			        rank[xset]=0;
			        return yset;
		        }else{
		        	parent[yset]=xset;
		        	rank[xset]+=rank[yset];
		        	rank[yset]=0;
		        	return xset;
		        }
		    }
		}
	  public static int[][] packU(int n, int[] from, int[] to, int max) {
		    
		    int[][] g = new int[n][];
		    int[] p = new int[n];
		    for (int i = 0; i < max; i++) p[from[i]]++;
		    for (int i = 0; i < max; i++) p[to[i]]++;
		    for (int i = 0; i < n; i++) g[i] = new int[p[i]];
		    for (int i = 0; i < max; i++) {
		        g[from[i]][--p[from[i]]] = to[i];
		        g[to[i]][--p[to[i]]] = from[i];
		    }
		    return g;
		}
		public static int[][] parents3(int[][] g, int root) {
		    int n = g.length;
		    int[] par = new int[n];
		    Arrays.fill(par, -1);
	 
		    int[] depth = new int[n];
		    depth[0] = 0;
	 
		    int[] q = new int[n];
		    q[0] = root;
		    for (int p = 0, r = 1; p < r; p++) {
		        int cur = q[p];
		        for (int nex : g[cur]) {
		            if (par[cur] != nex) {
		                q[r++] = nex;
		                par[nex] = cur;
		                depth[nex] = depth[cur] + 1;
		            }
		        }
		    }
		    return new int[][]{par, q, depth};
		}
		public static int lower_bound(int[] nums, int target) {
	        int low = 0, high = nums.length - 1;
	        while (low < high) {
	            int mid = low + (high - low) / 2;
	            if (nums[mid] < target)
	                low = mid + 1;
	            else
	                high = mid;
	        }
	        return nums[low] == target ? low : -1;
	    }
	 
	    public static int upper_bound(int[] nums, int target) {
	        int low = 0, high = nums.length - 1;
	        while (low < high) {
	            int mid = low + (high + 1 - low) / 2;
	            if (nums[mid] > target)
	                high = mid - 1;
	            else
	                low = mid;
	        }
	        return nums[low] == target ? low : -1;
	    }
	  public static boolean palin(String s)
		{
		   int i=0;
		   int j=s.length()-1;
		   while(i<j)
		   {
			   if(s.charAt(i)==s.charAt(j))
			   {
				   i++;
				   j--;
			   }
			   else return false;     
		   }
		   return true;
		}
		
	    static boolean CountPs(String s,int n)
	       {
	    	boolean b=false;
	    	     char[] S=s.toCharArray();
		       int[][] dp=new int[n][n];
		       boolean[][] p=new boolean[n][n];
		       for(int i=0;i<n;i++)p[i][i]=true;
		     
		       for(int i=0;i<n-1;i++)
		       {
		    	   if(S[i]==S[i+1])
		    	   {
		    		p[i][i+1]=true;
		    		dp[i][i+1]=1;
		    		b=true;
		    	   }
		       }
		    
		       for(int gap=2;gap<n;gap++)
		       {
		    	   for(int i=0;i<n-gap;i++)
		    	   {
		    		   int j=gap+i;
		    		   if(S[i]==S[j]&&p[i+1][j-1]){p[i][j]=true;}
		    		  
		    		  if(p[i][j])
		    			   dp[i][j]=dp[i][j-1]+dp[i+1][j]+1-dp[i+1][j-1];
		    		   
		    		   else  dp[i][j]=dp[i][j-1]+dp[i+1][j]-dp[i+1][j-1];
		    		  
		    		   if(dp[i][j]>=1){b=true;}
		    	   }
		       }
		      
		    return b; 
	   // return dp[0][n-1];
		       
	    }
	  
	  
	  
	 
	 
	public static int gcd(int a,int b)
	{
		int res=1;
		while(a>0)
		{
			res=a;
			a=b%a;
			b=res;
		}
		return res;
	}
	 
	 
	public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	public static long pow(long n,long p)
	{
		long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    p >>=1;
		    n*=n;
		}
		return result;
	 
	}
	 
	 
	 
	 
	static class Edge implements Comparator<Edge> {
		private int u;
		private int v;
		private int w;
		public Edge() {
		}
		public Edge(int u, int v, int w) {
			this.u=u;
			this.v=v;
			this.w=w;
		}
		public int getU() {
			return u;
		}
		public void setU(int u) {
			this.u = u;
		}
		public int getV() {
			return v;
		}
		public void setV(int v) {
			this.v = v;
		}
		public int getW() {
			return w;
		}
		public void setW(int w) {
			this.w = w;
		      }
		public int compareTo(Edge e)
		  {
			return this.getW() - e.getW();
		}
		@Override
		public String toString() {
			return "Edge [u=" + u + ", v=" + v + ", w=" + w + "]";
		}
		@Override
		public int compare(Edge arg0, Edge arg1) {
			// TODO Auto-generated method stub
			return 0;
		}
	}
	 
	 
	 
	static class Pair implements Comparable<Pair>
	{
		int a,b;
		Pair (int a,int b)
		{
			this.a=a;
			this.b=b;
		}
	 
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			if(this.a!=o.a)
			return -Integer.compare(this.a,o.a);
			else
				return -Integer.compare(this.b, o.b);
			//return 0;
		}
		public boolean equals(Object o) {
	       if (o instanceof Pair) {
	           Pair p = (Pair)o;
	           return p.a == a && p.b == b;
	       }
	       return false;
	   }
	   public int hashCode() {
	       return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
	   }
	}
	 
		static class InputReader
		{
			private InputStream stream;
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
			private SpaceCharFilter filter;
			
			public InputReader(InputStream stream)
			{
				this.stream = stream;
			}
			
			public int read()
			{
				if (numChars==-1) 
					throw new InputMismatchException();
				
				if (curChar >= numChars)
				{
					curChar = 0;
					try 
					{
						numChars = stream.read(buf);
					}
					catch (IOException e)
					{
						throw new InputMismatchException();
					}
					
					if(numChars <= 0)				
						return -1;
				}
				return buf[curChar++];
			}
		 
			public String nextLine()
			{
				BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
				String str = "";
	            try
	            {
	                str = br.readLine();
	            }
	            catch (IOException e)
	            {
	                e.printStackTrace();
	            }
	            return str;
			}
			public int ii()
			{
				int c = read();
				
				while(isSpaceChar(c)) 
					c = read();
				
				int sgn = 1;
				
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				
				int res = 0;
				do 
				{
					if(c<'0'||c>'9') 
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				while (!isSpaceChar(c)); 
				
				return res * sgn;
			}
			
			public long il() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				long res = 0;
				
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				while (!isSpaceChar(c));
					return res * sgn;
			}
			
			public double nextDouble() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				double res = 0;
				while (!isSpaceChar(c) && c != '.') 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, ii());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				if (c == '.') 
				{
					c = read();
					double m = 1;
					while (!isSpaceChar(c)) 
					{
						if (c == 'e' || c == 'E')
							return res * Math.pow(10, ii());
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						m /= 10;
						res += (c - '0') * m;
						c = read();
					}
				}
				return res * sgn;
			}
			
			public String readString() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = read();
				} 
				while (!isSpaceChar(c));
				
				return res.toString();
			}
		 
			public boolean isSpaceChar(int c) 
			{
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
		 
			public String next() 
			{
				return readString();
			}
			
			public interface SpaceCharFilter 
			{
				public boolean isSpaceChar(int ch);
			}
		}
	}
