#include <bits/stdc++.h>
#define pb push_back
#define fore(i,a,b) for(ll i=a,jet=b;i<jet;i++)
#define SZ(x) ((int)x.size());
#define ALL(x) x.begin(),x.end()
#define mset(a,v) memset((a),(v),sizeof(a))
#define fst first
#define snd second
#define imp(v) {for(auto i:v)cout<<i<<" ";cout<<"\n";}
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;
typedef vector<ll> vv;
const ll MAXF=1005,MOD=(119<<23)+1;
ll add(ll a, ll b){a+=b;if(a>=MOD)a-=MOD;return a;}
ll mul(ll a, ll b){return a*b%MOD;}
ll mem[MAXF][MAXF];
ll nCr(ll n, ll k){
if(n<0||k<0||n<k)return 0;
auto &res=mem[n][k];
if(res!=-1)return res;
if(n==0)return res=1;
return res=add(nCr(n-1,k-1),nCr(n-1,k));
}
ll n,m;
vector<vv> a;
vector<vv> pos;
ll doit(vv l, vv h, vv r){
// cerr<<"doit\n";
// imp(l)
// imp(h)
// imp(r)
ll res=1;
while(1){
ll cl=0,cr=0;
vector<vv> whs(2,vv(m));
vv goods(2,1);
fore(ty,0,2){
auto &wh=whs[ty];
auto &good=goods[ty];
ll val=a[0][(ty?r[0]:l[0])];
if(!ty&&l[0]>=h[0]){good=0;continue;}
if(ty&&r[0]>=n){good=0;continue;}
fore(i,0,m){
if(l[i]<h[i]&&a[i][l[i]]==val)wh[i]=0;
else if(r[i]<n&&a[i][r[i]]==val)wh[i]=1;
else {good=0;break;}
}
}
// imp(goods)
// fore(ty,0,2)imp(whs[ty])
if(!goods[0]&&!goods[1]){ // no puedo seguir
fore(i,0,m){ // quiero que haya terminado
if(l[i]<h[i]){res=0;break;}
if(r[i]<n){res=0;break;}
}
break;
}
fore(ty,0,2){ // sacamos wh[ty] mientras good
auto &wh=whs[ty];
auto &good=goods[ty];
auto &c=(ty?cr:cl);
while(good){
c++;
vv us(m);
fore(i,0,m){ // es good
if(wh[i]){
r[i]++;
// para la proxima
good&=r[i]<n;
us[i]=a[i][r[i]];
}
else {
l[i]++;
// para la proxima
good&=l[i]<h[i];
us[i]=a[i][l[i]];
}
}
good&=us==vv(m,us[0]);
}
}
ll cur=nCr(cl+cr,cl);
res=mul(res,cur);
}
// cout<<"= "<<res<<"\n\n";
return res;
}
ll f(vv l, vv r, vv h, vv vis){ // add cnt of rs in -1 for speedup
ll res=0;
if(count(ALL(vis),0)==0)return 1;
if(count(ALL(r),-1)==0)return doit(l,h,r);
fore(mn,0,n)if(!vis[mn]){
ll good=1;
fore(i,0,m){
if(a[i][l[i]]==mn)continue; // good
if(r[i]!=-1&&a[i][r[i]]!=mn){good=0;break;}
}
if(!good)continue;
vv nl=l,nr=r,nh=h;
vv nvis=vis; nvis[mn]=1;
fore(i,0,m){
if(a[i][nl[i]]==mn)nl[i]++;
else if(nr[i]==-1)nr[i]=(nh[i]=pos[i][mn])+1;
else nr[i]++;
}
res=add(res,f(nl,nr,nh,nvis));
}
return res;
}
int solve(int _n, int _m, vector<vector<int>>& _a)
{
mset(mem,-1);
n=_n,m=_m;
a.resize(m);
fore(i,0,m){
a[i]=vv(ALL(_a[i]));
for(auto &v:a[i])v--;
a[i].pb(n+i+1);
}
sort(ALL(a));
pos.resize(m);
fore(i,0,m){
pos[i].resize(n);
fore(j,0,n)pos[i][a[i][j]]=j;
}
ll res=f(vv(m),vv(m,-1),vv(m,-1),vv(n));
return res;
}
