#include <stdio.h>
#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define LC(x) (x<<1)
#define RC(x) ((x<<1)+1)
#define MID(x,y) ((x+y)>>1)
#define CLR(arr,val) memset(arr,val,sizeof(arr))
#define FAST_IO ios::sync_with_stdio(false);cin.tie(0);
typedef pair<int,int> pii;
typedef long long LL;
const double PI=acos(-1.0);
const int N=110;
const int M=N+N+N*N;
struct edge
{
    int to,nxt,cap,cost;
    edge(){}
    edge(int _to,int _nxt,int _cap,int _cost):to(_to),nxt(_nxt),cap(_cap),cost(_cost){}
};
edge E[M<<1];
int head[N<<1],tot;
int dis[N<<1],pre[N<<1],path[N<<1];
bitset<N<<1>vis;
char Mat[N][N];
int mc,mf,val[N];

void init()
{
    CLR(head,-1);
    tot=0;
    mc=mf=0;
}
inline void add(int s,int t,int cap,int cost)
{
    E[tot]=edge(t,head[s],cap,cost);
    head[s]=tot++;
    E[tot]=edge(s,head[t],0,-cost);
    head[t]=tot++;
}
int SPFA(int s,int t)
{
    CLR(dis,INF);
    vis.reset();
    queue<int>Q;
    dis[s]=0;
    vis[s]=1;
    Q.push(s);
    while (!Q.empty())
    {
        int u=Q.front();
        Q.pop();
        vis[u]=0;
        for (int i=head[u]; ~i; i=E[i].nxt)
        {
            int v=E[i].to;
            if(dis[v]>dis[u]+E[i].cost&&E[i].cap>0)
            {
                dis[v]=dis[u]+E[i].cost;
                pre[v]=u;
                path[v]=i;
                if(!vis[v])
                {
                    vis[v]=1;
                    Q.push(v);
                }
            }
        }
    }
    return dis[t]<0;
}
void MCMF(int s,int t)
{
    while (SPFA(s,t))
    {
        int Mf=INF;
        for (int i=t; i!=s; i=pre[i])
            Mf=min(Mf,E[path[i]].cap);
        for (int i=t; i!=s; i=pre[i])
        {
            E[path[i]].cap-=Mf;
            E[path[i]^1].cap+=Mf;
        }
        mf+=Mf;
        mc+=Mf*dis[t];
    }
}
int main(void)
{
    int n,i,j;
    while (~scanf("%d",&n)&&n)
    {
        init();
        for (i=1; i<=n; ++i)
            scanf("%d",&val[i]);
        int S=0,T=n+n+1;
        for (i=1; i<=n; ++i)
        {
            scanf("%s",Mat[i]+1);
            add(S,i,1,0);//n
            add(i+n,T,1,0);//n
            for (j=1; j<=n; ++j)
            {
                if(Mat[i][j]==‘1‘)
                    add(i,n+j,1,-(val[i]^val[j]));//n*n
            }
        }
        MCMF(S,T);
        printf("%d\n",-mc);
    }
    return 0;
}