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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.concurrent.LinkedBlockingDeque;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;


// graph, dfs,bfs, get connected components,iscycle, isbipartite, dfs on trees



public class scratch_25 {
    static class Graph{

        public static class Vertex{
            HashMap<Integer,Integer> nb= new HashMap<>();     // for neighbours of each vertex
        }

        public static HashMap<Integer,Vertex> vt;   // for vertices(all)

        public Graph(){
            vt= new HashMap<>();
        }

        public static int numVer(){
            return vt.size();
        }

        public static boolean contVer(int ver){
            return vt.containsKey(ver);
        }

        public static void addVer(int ver){
            Vertex v= new Vertex();
            vt.put(ver,v);
        }






        public static void addEdge(int ver1, int ver2, int weight){
            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }
            Vertex v1= vt.get(ver1);
            Vertex v2= vt.get(ver2);
            v1.nb.put(ver2,weight);                                 // if previously there is an edge, then this replaces that edge
            v2.nb.put(ver1,weight);
        }

        public static void delEdge(int ver1, int ver2){

            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }
            vt.get(ver1).nb.remove(ver2);
            vt.get(ver2).nb.remove(ver1);
        }
        public static void delVer(int ver){
            if(!vt.containsKey(ver)){
                return;
            }
            Vertex v1= vt.get(ver);
            ArrayList<Integer> arr= new ArrayList<>(v1.nb.keySet());
            for (int i = 0; i <arr.size() ; i++) {
                int s= arr.get(i);
                vt.get(s).nb.remove(ver);
            }
            vt.remove(ver);
        }
           static boolean done[];
            static int parent[];
            static ArrayList<Integer>vals= new ArrayList<>();


        public static boolean isCycle(int i){
            Stack<Integer>stk= new Stack<>();

            stk.push(i);
            while(!stk.isEmpty()){
                int x= stk.pop();
                vals.add(x);
             //   System.out.print("current="+x+" stackinit="+stk);
                if(!done[x]){
                    done[x]=true;
                }
                else if(done[x] ){
                    return true;
                }

                ArrayList<Integer>ar= new ArrayList<>(vt.get(x).nb.keySet());
                for (int j = 0; j <ar.size() ; j++) {
                   if(parent[x]!=ar.get(j)){
                       parent[ar.get(j)]=x;
                    stk.push(ar.get(j));
                   }
                }
               // System.out.println(" stackfin="+stk);
            }
            return false;
        }
        static int distance[];
        static ArrayList<Integer>ans= new ArrayList<>();
        public static boolean dfs1(int p, int col[], int pcol){

            Stack<Integer>stk= new Stack<>();
            stk.add(p);
            while(!stk.isEmpty()){
                int x= stk.pop();
             //   System.out.println("x="+x);
                if(!done[x]){
                    done[x]=true;
                }
                if(col[x]!=pcol){
                    return false;
                }
                ArrayList<Integer>v= new ArrayList<>(vt.get(x).nb.keySet());
                for (int i = 0; i <v.size() ; i++) {
                    int c= v.get(i);
                    if(!done[c]){
                    stk.add(c);
                    }
                }
            }
            return true;
        }
        public static boolean dfs(int v, int[]col){
            done[v]=true;
            ArrayList<Integer>ar=new ArrayList<>(vt.get(v).nb.keySet());
            for (int i = 0; i <ar.size() ; i++) {
                int x= ar.get(i);
                if(!done[x]){
                    done[x]=true;
                  //  System.out.println("x="+x);
                    boolean d= dfs1( x,col,col[x]);
                    //System.out.println("x="+x+"d="+d);
                    if(!d){
                        return false;
                    }
                }
            }
            return true;
        }






        }
    static class DisjointSet{
        HashMap<Integer,Node> mp= new HashMap<>();

        public static class Node{
            int data;
            Node parent;
            int rank;
        }


        public void create(int val){
            Node nn= new Node();
            nn.data=val;
            nn.parent=nn;
            nn.rank=0;
            mp.put(val,nn);
        }

        public int findparent(int val){

            return findparentn(mp.get(val)).data;

        }


        public Node findparentn(Node n){
            if(n==n.parent){
                return n;
            }
            Node rr= findparentn(n.parent);
            n.parent=rr;
            return rr;
        }



        public void union(int val1, int val2){                                                                               // can also be used to check cycles

            Node n1= findparentn(mp.get(val1));
            Node n2= findparentn(mp.get(val2));


            if(n1.data==n2.data) {
                return;
            }



            if(n1.rank<n2.rank){
                n1.parent=n2;
            }

            else if(n2.rank<n1.rank){
                n2.parent=n1;
            }

            else {
                n2.parent=n1;
                n1.rank++;
            }

        }
    }
    static class Pair implements Comparable<Pair>{
        long x;
        long y;
        public Pair(long x,long y){
            this.x=x;
            this.y=y;
        }
        @Override
        public int compareTo(Pair o){
            return (int)this.y-(int)o.y;


        }
        @Override
        public boolean equals(Object me) {
            Pair binMe = (Pair)me;
            if(this.x==binMe.x && this.y==binMe.y)
                return true;
            else
                return false;
        }

        @Override
        public int hashCode() {
            return (int)this.x + (int)this.y;
        }

        @Override
        public String toString() {
            return x+" "+y;
        }


    }



    // int count=0;
    //static long count=0;
    static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }




    // After writing solution, quick scan for:
    //   array out of bounds
    //   special cases e.g. n=1?
    //
    // Big numbers arithmetic bugs:
    //   int overflow
    //   sorting, or taking max, or negative after MOD
    public static void main(String[] args)  throws IOException {
        Reader.init(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
       int n= Reader.nextInt();
       int arr[]= new int[n];
        for (int i = 0; i <n ; i++) {
            arr[i]= Reader.nextInt();
        }
        char ar[][]= new char[n][n];
        for (int i = 0; i <n ; i++) {
            ar[i]= Reader.next().toCharArray();
        }

        DisjointSet set= new DisjointSet();
        for (int i = 0; i <n ; i++) {
            set.create(i);
        }
        for (int i = 0; i <n ; i++) {
            for (int j = 0; j <n ; j++) {
                if(ar[i][j]=='1'){
                    set.union(i,j);
                }
            }
        }
        HashMap<Integer, ArrayList<Integer>>ind= new HashMap<>();
        HashMap<Integer, ArrayList<Integer>>vals= new HashMap<>();
        for (int i = 0; i <n ; i++) {
            int x= set.findparent(i);
            if(!ind.containsKey(x)){
                ArrayList<Integer>a= new ArrayList<>();
                ArrayList<Integer>b= new ArrayList<>();
                a.add(i);
                b.add(arr[i]);
                ind.put(x,a);
                vals.put(x,b);
            }
            else{
                ArrayList<Integer>a= ind.get(x);
                ArrayList<Integer>b= vals.get(x);
                a.add(i);
                b.add(arr[i]);
                ind.put(x,a);
                vals.put(x,b);
            }
        }

        ArrayList<Integer>v= new ArrayList<>(ind.keySet());
        for (int i = 0; i <v.size() ; i++) {
            int x= v.get(i);
            ArrayList<Integer>a= new ArrayList<>(ind.get(x));
            ArrayList<Integer>b= new ArrayList<>(vals.get(x));
            Collections.sort(a);
            Collections.sort(b);
            ind.put(x,a);
            vals.put(x,b);
        }
//        System.out.println(ind);
//        System.out.println(vals);
        int ans[]= new int[n];
        for (int i = 0; i <v.size() ; i++) {
            int x= v.get(i);
            ArrayList<Integer>a= new ArrayList<>(ind.get(x));
            ArrayList<Integer>b= new ArrayList<>(vals.get(x));
            for (int j = 0; j <a.size() ; j++) {
                ans[a.get(j)]=b.get(j);
            }

        }
        //System.out.println(Arrays.toString(ans));
        for (int i = 0; i <n ; i++) {
            out.append(ans[i]+" ");
        }








        
        out.flush();
        out.close();

    }



    static long modExp(long a, long b, long mod) {
        //System.out.println("a is " + a + " and b is " + b);
        if (a==1) return 1;
        long ans = 1;
        while (b!=0) {
            if (b%2==1) {
                ans = (ans*a)%mod;
            }
            a = (a*a)%mod;
            b/=2;
        }
        return ans;
    }


    public static long modmul(long a, long b, long mod) {
        return b == 0 ? 0 : ((modmul(a, b >> 1, mod) << 1) % mod + a * (b & 1)) % mod;
    }

    static long sum(long n){
        //   System.out.println("lol="+ (n*(n-1))/2);
        return (n*(n+1))/2;
    }






    public static ArrayList<Integer> Sieve(int n) {
        boolean arr[]= new boolean [n+1];
        Arrays.fill(arr,true);
        arr[0]=false;
        arr[1]=false;
        for (int i = 2; i*i <=n ; i++) {
            if(arr[i]){
                for (int j = 2; j <=n/i ; j++) {
                    int u= i*j;
                    arr[u]=false;
                }}
        }
        ArrayList<Integer> ans= new ArrayList<>();
        for (int i = 0; i <n+1 ; i++) {
            if(arr[i]){
                ans.add(i);
            }
        }
        return ans;
    }




    static long power( long x, long y, long p)
    {

        long res = 1;


        x = x % p;

        if (x == 0) return 0;

        while (y > 0)
        {

            if((y & 1)==1)
                res = (res * x) % p;


            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    public static long ceil_div(long a, long b){
        return (a+b-1)/b;
    }

    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long lcm(long a, long b)
    {
        return (a*b)/gcd(a, b);
    }

}