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.
import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.MathContext;

import javax.swing.plaf.synth.SynthSeparatorUI;

import org.xml.sax.HandlerBase;

import java.util.*;

public class Main {
	
	static HashMap<Integer, Integer> map = new HashMap<>();
    public static void main(String[] args) {
        FasterScanner s = new FasterScanner();
        PrintWriter out=new PrintWriter(System.out);
        int n=s.nextInt();
        
        int [] a  = s.nextIntArray(n);
        int[][] m = new int[n][n];
        
        for(int i=0;i<n;i++){
        	char[] b= s.nextLine().toCharArray();
        	for(int j=0;j<n;j++)
        		if(b[j]=='1')
        			m[i][j]=1;
        }
        boolean [] done = new boolean[n];
        for(int i=0;i<n;i++){
        	if(done[i]) continue;
        	done[i]=true;
        	int[] val = new int[n];
        	int[] pos = new int[n];
        	int count=0;
        	int ptr=0;
        	val[count]=a[i];
        	pos[count++]=i;
        	while(ptr<count){
        		int k=pos[ptr];
        		for(int j=0;j<n;j++){
        			if(m[k][j]==1 && !done[j]){
        				val[count]=a[j];
        				pos[count++]=j;
        				done[j]=true;
        			}
        		}
        		ptr++;
        	}
        	val = Arrays.copyOf(val, count);
        	pos = Arrays.copyOf(pos, count);
        	Arrays.sort(val);
        	Arrays.sort(pos);
        	for(int j=0;j<count;j++)
        		a[pos[j]]=val[j];
        	
        }
        
        for(int i=0;i<n;i++)
        	out.print(a[i]+" ");
        out.close();
    }
    static class Matrix {
    	public static int[][] matrixAdd(int[][] a, int[][] b) {
    		int n = a.length;
    		int m = a[0].length;
    		int[][] res = new int[n][m];
    		for (int i = 0; i < n; i++) {
    			for (int j = 0; j < m; j++) {
    				res[i][j] = a[i][j] | b[i][j];
    			}
    		}
    		return res;
    	}

    	public static int[][] matrixMul(int[][] a, int[][] b) {
    		int n = a.length;
    		int m = a[0].length;
    		int k = b[0].length;
    		int[][] res = new int[n][k];
    		for (int i = 0; i < n; i++) {
    			for (int j = 0; j < k; j++) {
    				for (int p = 0; p < m; p++) {
    					res[i][j] = res[i][j] | (a[i][p] & b[p][j]);
    				}
    			}
    		}
    		return res;
    	}

    	public static int[][] matrixPow(int[][] a, int p) {
    		if (p == 0) {
    			return matrixUnit(a.length);
    		} else if (p % 2 == 0) {
    			return matrixPow(matrixMul(a, a), p / 2);
    		} else {
    			return matrixMul(a, matrixPow(a, p - 1));
    		}
    	}

    	public static int[][] matrixPowSum(int[][] a, int p) {
    		int n = a.length;
    		if (p == 0) {
    			return new int[n][n];
    		}
    		if (p % 2 == 0) {
    			return matrixMul(matrixPowSum(a, p / 2), matrixAdd(matrixUnit(n), matrixPow(a, p / 2)));
    		} else {
    			return matrixAdd(a, matrixMul(matrixPowSum(a, p - 1), a));
    		}
    	}

    	public static int[][] matrixUnit(int n) {
    		int[][] res = new int[n][n];
    		for (int i = 0; i < n; ++i) {
    			res[i][i] = 1;
    		}
    		return res;
    	}

    	// Usage example
    	public static void main(String[] args) {
    		int[][] a = { { 1, 2 }, { 3, 4 } };
    		int[][] b = matrixUnit(2);
    		int[][] c = matrixMul(a, b);
    	}
    }

    
    
    
    
    
    
    
    static class Node
    {
    	int id=0;
    	char ch;
    	boolean done=false;
    	Node l,r;
    	int parent=0;
    	Node(char ch){ this.ch=ch;}
		
    }
    static int gcd (long m, long n){
        long x;
        long y;
        while(m%n != 0){
            x = n;
            y = m%n;
            m = x;
            n = y;
        }
        return (int) n;
    }

    
    
    
    public static class st {
    	
	    int n;
	    int[] t;
	   
	    void build(int n2) {  // build the tree
	       t=new int[2*n2];
	       n=n2;
	    }
	    void modify(int p, int value) {
	      for (t[p += n] += value; p > 1; p >>= 1) t[p>>1] = t[p] + t[p^1];
	    }
	    int query(int l, int r) {  // sum on interval [l, r)
	      int res=0;
	      for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
	            if ((l&1)!=0) res+=t[l++];
	            if ((r&1)!=0) res+=t[--r];
	          }
	      return res;
	    }
	}
    
  
   
   
   
   
   
   
   
   
   
   
    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            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 long nextLong() {
            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 int nextInt() {
            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 int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
      
        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}