#include<bits/stdc++.h>
typedef long long ll;
using namespace std;
int read()
{
	int ret=0;bool f=0;char c=getchar();
	while(c>'9'||c<'0')f|=(c=='-'),c=getchar();
	while(c>='0'&&c<='9')ret=(ret<<3)+(ret<<1)+(c^48),c=getchar();
	return f?-ret:ret;
}
const int maxn=505,maxm=2000,mod=998244353;
int qpow(int a,int b){int ret=1;for(;b;b>>=1,a=(ll)a*a%mod)if(b&1)ret=(ll)ret*a%mod;return ret;}
int n,k;
int val[maxn][maxn];
bitset<maxm>exi[maxn];
struct edge{int fr,to,val;}e[maxn*maxn];int cnt;
struct dsu
{
	int fa[maxn];
	void prework(){iota(fa+1,fa+n+1,1);}
	int get(int x){return x==fa[x]?x:fa[x]=get(fa[x]);}
	void merge(int x,int y){fa[get(x)]=get(y);}
	bool check(int x,int y){return get(x)==get(y);}
}S;
struct matrix
{
	int num[maxn][maxn];
	void clear(){memset(num,0,sizeof num);}
	int*operator[](const int &i){return num[i];}
	int calc(int n)
	{
		int ret=1;
		for(int i=1;i<=n;i++)
		{
			int pos=-1;
			for(int j=i;j<=n;j++)if(num[j][i]){pos=j;break;}
			if(pos==-1)return 0;
			if(pos!=i){swap(num[pos],num[i]);ret=mod-ret;}
			ret=(ll)ret*num[i][i]%mod;
			int inv=qpow(num[i][i],mod-2);
			for(int j=i;j<=n;j++)num[i][j]=(ll)num[i][j]*inv%mod;
			for(int j=i+1;j<=n;j++)
				if(num[j][i])
				{
					int tmp=num[j][i];
					for(int k=i;k<=n;k++)
						(num[j][k]+=mod-(ll)num[i][k]*tmp%mod)%=mod;
				}
		}
		return ret;
	}
}A;
int get()
{
	int ret=1;
	S.prework();
	for(int i=1;i<=cnt;i++)
	{
		if(i!=1&&e[i].val==e[i-1].val)continue;
		map<int,int>id;int num=0;A.clear();
		for(int j=i;j<=cnt;j++)
		{
			if(e[j].val!=e[i].val)break;
			if(S.check(e[j].fr,e[j].to))continue;
			if(!id.count(S.get(e[j].fr)))id[S.get(e[j].fr)]=++num;
			if(!id.count(S.get(e[j].to)))id[S.get(e[j].to)]=++num;
			(A[id[S.get(e[j].fr)]][id[S.get(e[j].to)]]+=mod-val[e[j].fr][e[j].to])%=mod;
			(A[id[S.get(e[j].to)]][id[S.get(e[j].fr)]]+=mod-val[e[j].fr][e[j].to])%=mod;
			(A[id[S.get(e[j].to)]][id[S.get(e[j].to)]]+=val[e[j].fr][e[j].to])%=mod;
			(A[id[S.get(e[j].fr)]][id[S.get(e[j].fr)]]+=val[e[j].fr][e[j].to])%=mod;
		}
		for(int j=i;j<=cnt;j++)
		{
			if(e[j].val!=e[i].val)break;
			S.merge(e[j].fr,e[j].to);
		}
		static bool vis[maxn];
		for(auto &j:id)
			if(!vis[S.get(j.first)])
			{
				vis[S.get(j.first)]=1;
				A[j.second][j.second]++;
			}
		for(auto &j:id)vis[S.get(j.first)]=0;
		ret=(ll)ret*A.calc(num)%mod;
	}
	return ret;
}
int main()
{
	freopen("treecnt.in","r",stdin);
	freopen("treecnt.out","w",stdout);
	n=read();k=read();
	for(int i=1;i<n;i++)
		for(int j=i+1;j<=n;j++)val[i][j]=val[j][i]=read();
	int sum=0;
	for(int i=0;i<k;i++)
	{
		string s;cin>>s;
		bool flag=0;
		for(int j=1;j<=n;j++)
			if(s[j-1]=='1')exi[j][i]=1,sum++;
		if(s.find('1')!=s.npos)sum--;
	}
	for(int i=1;i<=n;i++)
		for(int j=i+1;j<=n;j++)
			e[++cnt]={i,j,(int)((exi[i]&exi[j]).count())};
	sort(e+1,e+cnt+1,[](edge &i,edge &j){return i.val>j.val;});
	S.prework();
	for(int i=1;i<=cnt;i++)
		if(!S.check(e[i].fr,e[i].to))
		{
			sum-=e[i].val;
			S.merge(e[i].fr,e[i].to);
		}
	if(sum){puts("0");return 0;}
	printf("%d\n",get());
	return 0;
}