#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <set>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <algorithm>
#include <limits>
using namespace std;
typedef long long LL;
const int MAXN=210;
const int MAXM=1e+4;
const int INF= numeric_limits<int>::max();
const LL LL_INF= numeric_limits<LL>::max();
struct Edge
{
int from,to,ci,cost,next;
Edge(){}
Edge(int _from,int _to,int _ci,int _cost,int _next):from(_from),to(_to),ci(_ci),cost(_cost),next(_next){}
}e[MAXM];
int head[MAXN],tot;
int q[MAXM];
int dis[MAXN],pre[MAXN],rec[MAXN],vis[MAXN];
inline void init(){
memset(head,-1,sizeof(head));
tot=0;
}
inline void AddEdge1(int u,int v,int ci,int cost){
e[tot]=Edge(u,v,ci,cost,head[u]);
head[u]=tot++;
e[tot]=Edge(v,u,0,-cost,head[v]);
head[v]=tot++;
}
inline bool spfa(int S,int T,LL &cost,LL &flow){
int i,h=0,t=0;
for(i=0;i<=MAXN;i++){
dis[i]=INF;
vis[i]=false;
}
q[h]=S;
dis[S]=0;
vis[S]=true;
while(h<=t){
int u=q[h++];
vis[u]=false;
for(i=head[u];~i;i=e[i].next){
int v=e[i].to;
if(e[i].ci>0&&dis[v]>dis[u]+e[i].cost){
dis[v]=dis[u]+e[i].cost;
pre[v]=u;
rec[v]=i;
if(!vis[v]){
vis[v]=1;
q[++t]=v;
}
}
}
}
if(dis[T]==INF)return false;
if(dis[T]>=0)return false;
int minn=INF;
for(i=T;i!=S;i=pre[i]){
if(e[rec[i]].ci<minn)
minn=e[rec[i]].ci;
}
for(i=T;i!=S;i=pre[i]){
e[rec[i]].ci-=minn;
e[rec[i]^1].ci+=minn;
}
cost+=dis[T]*minn;
flow+=minn;
return true;
}
inline void mincostmaxflow(int S,int T,LL &cost,LL &flow){
while(spfa(S,T,cost,flow));
}
int v[MAXN];
int main()
{
int n;
while(~scanf("%d",&n)){
if(n==0)break;
for(int i=1;i<=n;i++)scanf("%d",&v[i]);
init();
for(int i=1;i<=n;i++){
for(int j=1;j<=n;j++){
char x;
scanf(" %c",&x);
if(x=='1')AddEdge1((i<<1),(j<<1)|1,1,-(v[i]^v[j]));
}
}
for(int i=1;i<=n;i++){
AddEdge1(0,(i<<1),1,0);
AddEdge1((i<<1)|1,1,1,0);
}
LL cost=0,flow=0;
mincostmaxflow(0,1,cost,flow);
cost=-cost;
printf("%I64d\n",cost);
}
return 0;
}
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