#include <bits/stdc++.h>
#define INF 1000000000
#define LINF 1000000000000000000
#define mod 998244353
#define F first
#define S second
#define ll int
#define N 3010
#define M 10000010
using namespace std;
mt19937_64 rnd(114514);
ll ksm(ll x,ll y)
{
	ll ret=1;
	while(y)
	{
		if(y&1)
		{
			ret=(1ll*ret*x)%mod;
		}
		x=(1ll*x*x)%mod;
		y>>=1;
	}
	return ret;
}
ll n,k,fa[M],p[N][N],f[N],g[N],val[M][2];
ll getf(ll x){return x==fa[x]?x:fa[x]=getf(fa[x]);}
void update()
{
	ll i,j;
	for(i=0;i<n;i++)
	{
		for(j=0;j<n;j++)
		{
			if(i!=j)
			{
				fa[getf(i*n+j)]=getf(f[i]*n+f[j]);
			}
		}
	}
	return;
}
using Ele=vector<int>;
Ele comp(int n,Ele x,Ele y){
   Ele z(n);
   for(int i=0;i<n;i++)z[i]=x[y[i]];
   return z;
}
Ele inv(int n,Ele x){
   Ele z(n);
   for(int i=0;i<n;i++)z[x[i]]=i;
   return z;
}
long long anss=0;
void work()
{
   int m;m=k;
   vector<Ele>a(m,Ele(n));
   vector<int>ans{1};
   int aa=0;
   for(auto&pp:a)
   {
   	int bb=0;
  		for(int&x:pp) x=p[aa][bb],++bb;
  		++aa;
  	}
   for(;n>1;n--){
      vector<Ele>f(n);
      f[0].resize(n);
      for(int i=0;i<n;i++)f[0][i]=i;
      queue<int>q;q.push(0);
      for(;!q.empty();){
         int u=q.front();q.pop();
         for(const auto&p:a)if(f[p[u]].empty())
         f[p[u]]=comp(n,p,f[u]),q.push(p[u]);
      }
      int r=count_if(begin(f),end(f),[](const auto&p){return!p.empty();});
      for(int i=0,w=0;i<ans.size()||w;i++){
         if(i==ans.size())ans.push_back(0);
         int a=(w+ans[i]*r)%10,b=(w+ans[i]*r)/10;
         ans[i]=a,w=b;
      }
      for(int i=0;i<n;i++)if(!f[i].empty())f[i]=inv(n,f[i]);
      vector<Ele>b;
      for(int t=n*2;t--;){
         Ele p=f[0];
         for(int i=1;i<=10;i++){
            shuffle(begin(a),end(a),rnd);
            for(const auto&x:a)if(rnd()&1)p=comp(n,p,x);
         }
         p=comp(n,f[p[0]],p);
         p.erase(begin(p));
         for(int&x:p)x--;
         b.push_back(p);
      }a=b;
   }
   reverse(begin(ans),end(ans));
   for(int x:ans)anss=(anss*10+x)%mod;
}
int main(){
	ll i,j,t;
	scanf("%d%d",&n,&k);
	for(i=0;i<k;i++)
	{
		for(j=0;j<n;j++)
		{
			scanf("%d",&p[i][j]);
			p[i][j]--;
		}
	}
	for(i=0;i<n*n;i++)
	{
		fa[i]=i;
	}
	for(t=0;t<40;t++)
	{
		for(i=0;i<n;i++)
		{
			f[i]=i;
		}
		for(i=0;i<k;i++)
		{
			if(rnd()&1)
			{
				for(j=0;j<n;j++)
				{
					g[j]=f[p[i][j]];
				}
				for(j=0;j<n;j++)
				{
					f[j]=g[j];
				}
			}
		}
		update();
	}
	for(i=0;i<n;i++)
	{
		for(j=0;j<n;j++)
		{
			if(i==j)
			{
				continue;
			}
			val[getf(i*n+j)][i>j]++;
		}
	}
	ll ans=0;
	for(i=0;i<n*n;i++)
	{
		if(val[i][0]||val[i][1])
		{
			ans=(ans+((1ll*((1ll*val[i][0]*val[i][1])%mod)*ksm((val[i][0]+val[i][1])%mod,mod-2))%mod))%mod;
		}
	}
	work();
//	cout<<ans<<" "<<anss<<"\n";
	ans=ans*anss%mod;
	printf("%d\n",(ans%mod+mod)%mod);
	return 0;
}