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.*; 
import java.util.ArrayList;
import java.util.Collections;

public class NewYearPermutation {
    
    public static void dfs(boolean[][] a, boolean skip[], int base, int next){
        if(!skip[next]){skip[next] = true;}else return;
        for(int j=1;j<=a.length-1;++j){
            if(a[next][j]){  
                for(int k=1;k<=a.length-1;++k){
                    a[base][k] |= a[j][k];
                }  
                dfs(a, skip, base, j);
            }
        }
    } 
    
    public static void main(String[] args) throws Exception{  
        int N = IO.readInt();
        int[] numbers = IO.readIntArray(N, " ");
        boolean[][] matrix = IO.read2dBooleanArray(N, N, "");  
        boolean[] skip = new boolean[N+1];  
        
        for(int i=1;i<=N;++i) {dfs(matrix, skip, i, i);}  
          
        for(int i=1;i<=N;++i){
            ArrayList<Integer> a = new ArrayList<>();
            for(int j=1;j<=N;++j){
                if(matrix[i][j])a.add(numbers[j]);
            }
            Collections.sort(a);
            int k=0;
            for(int j=1;j<=N;++j){
                if(matrix[i][j])numbers[j] = a.get(k++);
            }
        }
        IO.printIntArray(numbers);
    }
      
    static class IO {
        static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public static int[][] read2dInt (int rows, int cols, String seperator) throws Exception{
            int[][] arr = new int[rows+1][cols+1];
            for(int i=1;i<=rows;++i){
                arr[i] = readIntArray(cols, seperator);
            }
            return arr;
        }
        
        public static boolean[][] read2dBooleanArray(int rows, int cols, String seperator) throws IOException{
            boolean[][] arr = new boolean[rows+1][cols+1];
            for(int i=1;i<=rows;++i){
                arr[i] = readBooleanArray(cols, seperator);
            }
            return arr;
        }
        
        public static int[] readIntArray(int nInts, String seperator) throws IOException{
            String ints = br.readLine();
            String[] sArray = ints.split(seperator);
            int[] array = new int[nInts+1];
            for(int i=1;i<=nInts;++i)array[i] = Integer.parseInt(sArray[i-1]);
            return array;
        }

        public static boolean[] readBooleanArray(int nBooleans, String seperator) throws IOException{
            String booleans = br.readLine();
            String[] sArray = booleans.split(seperator);
            boolean[] array = new boolean[nBooleans+1];
            for(int i=1;i<=nBooleans;++i){array[i] = sArray[i-1].matches("1");}
            return array;
        }
        
        public static long[] readLongArray(int nLongs, String seperator) throws IOException{
            String longs = br.readLine();
            String[] sArray = longs.split(seperator);
            long[] array = new long[nLongs+1];
            for(int i=1;i<=nLongs;++i)array[i] = Long.parseLong(sArray[i-1]);
            return array;
        }

        public static double[] readDoubleArray(int nDoubles, String seperator) throws IOException{
            String doubles = br.readLine();
            String[] sArray = doubles.split(seperator);
            double[] array = new double[nDoubles+1];
            for(int i=1;i<=nDoubles;++i)array[i] = Double.parseDouble(sArray[i-1]);
            return array;
        }

        public static char[] readCharArray(int nChars, String seperator) throws IOException{
            String chars = br.readLine();
            String[] sArray = chars.split(seperator);
            char[] array = new char[nChars+1];
            for(int i=1;i<=nChars;++i)array[i] = sArray[i-1].charAt(0);
            return array;
        }

        public static int readInt() throws IOException{
            String in = br.readLine();
            return Integer.parseInt(in);
        }

        public static double readDouble() throws IOException{
            String in = br.readLine();
            return Double.parseDouble(in);
        }

        public static long readLong() throws IOException{
            String in = br.readLine();
            return Long.parseLong(in);
        }

        public static int readChar() throws IOException{
            String in = br.readLine();
            return in.charAt(0);
        }

        public static void print(Object... o){
            for(Object os:o) System.out.print(os);
        }

        public static void println(Object... o){
            for(Object os:o) System.out.print(os);
            System.out.print("\n");
        }

        public static void printIntArray(int[] o){
            for(int i = 1;i<=o.length-1;++i)IO.print(o[i]+" ");
            IO.println();
        }
        
        
        public static void printlnSeperate(String seperator, Object... o){
            StringBuilder sb = new StringBuilder(); 
            sb.delete(sb.length()-seperator.length(), sb.length());
            System.out.println(sb);
        }
    }
}

