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.
'''
Created on 13/12/2017

@author: 

XXX: http://codeforces.com/problemset/problem/500/B
XXX: https://github.com/imressed/python-disjoint-set/blob/master/disjoint_set.py
XXX: https://gist.github.com/isaacl/7561953
XXX: https://codereview.stackexchange.com/questions/79208/disjoint-set-data-structure-in-python-3
'''

import logging
import sys
from asyncio.log import logger
from _operator import pos

nivel_log = logging.ERROR
nivel_log = logging.DEBUG
logger_cagada = None

# Python3 port of http://algs4.cs.princeton.edu/code/edu/princeton/cs/algs4/UF.java.html
class DisjointSet:
    """
    Execution:    python disjoint_set.py < input.txt
    Data files:   http://algs4.cs.princeton.edu/15uf/tinyUF.txt
                  http://algs4.cs.princeton.edu/15uf/mediumUF.txt
                  http://algs4.cs.princeton.edu/15uf/largeUF.txt
    
    Weighted quick-union by rank with path compression.
    
    % python disjoint_set.py < tinyUF.txt
    4 3
    3 8
    6 5
    9 4
    2 1
    5 0
    7 2
    6 1
    2 components
    """
    def __init__(self, n):
        # number of components
        self.count = n 
        # parent[i] = parent of i
        self.parent = list(range(n))
        # rank[i] = rank of subtree rooted at i (never more than 31)
        self.rank = [0] * n  
        self.es_raiz = set(list(range(n)))
        self.llaves = [set([x]) for x in range(n)]
        
    def find(self, p):
        """Returns the component identifier for the component 
        containing site p.
        
        Args:
            p (int): the integer representing one site
        
        Returns:
            int. the component identifier for the component containing site p
        """
        self.validate(p)
        if p != self.parent[p]:
            self.parent[p] = self.find(self.parent[p])  # path compression
        return self.parent[p]

    
    def connected(self, p, q):
        """Returns true if the the two sites are in the same component.
        
        Args:
            p (int): the integer representing one site
            q (int): the integer representing the other site
            
        Returns:
            Boolean. true if the two sites p and q are in the same component;
                false otherwise.
        """
        return self.find(p) == self.find(q)
        
    def union(self, p, q):
        """Merges the component containing site p with the 
        the component containing site q.
        
        Args:
            p (int): the integer representing one site
            q (int): the integer representing the other site
        """
        rootP = self.find(p)
        rootQ = self.find(q)
        if rootP == rootQ: return
        
        # make root of smaller rank point to root of larger rank
        if self.rank[rootP] < self.rank[rootQ]:
            self.parent[rootP] = rootQ
            self.es_raiz.remove(rootP)
            self.llaves[rootQ] |= self.llaves[rootP]
        else:
            if self.rank[rootP] > self.rank[rootQ]:
                self.parent[rootQ] = rootP
            else:
                self.parent[rootQ] = rootP
                self.rank[rootP] += 1
            self.es_raiz.remove(rootQ)
            self.llaves[rootP] |= self.llaves[rootQ]
        self.count -= 1

    def validate(self, p):
        """validate that p is a valid index"""
        n = len(self.parent)
        if p < 0 or p >= n:
            raise IndexError("index {} is not between 0 and {}".format(p, n - 1)) 
        
    def raices(self):
        return list(self.es_raiz)
    def llaves_en_conjuntos_disjuntos(self):
        return [self.llaves[x] for x in self.raices()]

def perputa_ano_nuevo_core(nodos_tam, llaves, ariscas):
    caca = DisjointSet(nodos_tam)
    for arisca in ariscas:
        if caca.connected(arisca[0], arisca[1]):
            continue
        caca.union(arisca[0], arisca[1])
    #logger_cagada.debug("las racies son {}".format(caca.raices()))
    #logger_cagada.debug("los conjuntos son {}".format(caca.llaves_en_conjuntos_disjuntos()))
    for monton in caca.llaves_en_conjuntos_disjuntos():
        nums_en_posiciones = []
        for pos_act in monton:
            nums_en_posiciones.append(llaves[pos_act])
        #logger_cagada.debug("los nums en pos {} son {}".format(monton, nums_en_posiciones))
        nums_en_posiciones.sort()
        idx_num = 0
        for pos_act in sorted(monton):
            llaves[pos_act] = nums_en_posiciones[idx_num]
            idx_num += 1
    #logger_cagada.debug("las llaves aora {}".format(llaves))
    return llaves
        

def caca_comun_lee_linea_como_num():
    return int(sys.stdin.readline().strip())

def caca_comun_lee_linea_como_monton_de_numeros():
    return list(map(int, sys.stdin.readline().strip().split(" ")))

def perputa_ano_nuevo_main():
    nodos_tam = caca_comun_lee_linea_como_num()
    llaves = caca_comun_lee_linea_como_monton_de_numeros()
    ariscas = []
    for i in range(nodos_tam):
        miedas = sys.stdin.readline().strip()
        #logger_cagada.debug("puta mierda {}".format(miedas))
        for j in range(nodos_tam):
            if miedas[j] == '1':
                ariscas.append((i, j))
        if not i:
#            assert ariscas
            pass
    #logger_cagada.debug("las ariscas {}".format(ariscas))
    fuck = perputa_ano_nuevo_core(nodos_tam, llaves, ariscas)
    print("{}".format(" ".join(map(str, fuck))))

if __name__ == '__main__':
        FORMAT = "[%(filename)s:%(lineno)s - %(funcName)20s() ] %(message)s"
        logging.basicConfig(level=nivel_log, format=FORMAT)
        logger_cagada = logging.getLogger("asa")
        logger_cagada.setLevel(nivel_log)
        perputa_ano_nuevo_main()
