#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 55,M = 10,mod = 998244353;
int addv(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
int subv(int x,int y){return (x>=y)?(x-y):(x-y+mod);}
void add(int& x,int y){x = addv(x,y);}
void sub(int& x,int y){x = subv(x,y);}
int qpow(int a,int n){
    int res = 1; a%=mod;
    while(n){
        if(n&1)res = 1ll*res*a%mod;
        n>>=1; a = 1ll*a*a%mod;
    }
    return res;
}
int qinv(int a){return qpow(a,mod-2);}
//
int n,m,q;

map<int,int> tF,id; set<int> tR;
int val[M],R[N],cnt,U,lim;
int buc[M][N],tot;

int f[N][N][1<<M],g[N][1<<M],fac[N],rfac[N];

int vx[M],vy[M],vw[M];

int xv[N][N][1<<M],pw[N];

int main(){
    cin>>n>>m>>q;
    fac[0] = rfac[0] = 1; for(int i=1;i<=n;i++)fac[i] = 1ll*fac[i-1]*i%mod,rfac[i] = qinv(fac[i]);

    for(int i=0,x,y,w;i<q;i++){
        cin>>x>>y>>w; vx[i] = x,vy[i] = y,vw[i] = w;
        if(tF.find(y) == tF.end())tF[y] = w;
        else tF[y] = min(tF[y],w);
    }
    for(auto [p,w] : tF)id[p] = cnt,val[cnt++] = w;
    for(int i=0;i<q;i++)tR.insert(vx[i]);
    for(auto r : tR){
        for(int i=0;i<q;i++)if(vx[i] == r)buc[tot][vw[i]] = id[vy[i]]+1;
        tot++;
    }
    //
    U = (1<<cnt)-1,lim = n-cnt;

    //预处理一些系数
    for(int i=1;i<=n;i++)for(int j=0;j<=lim;j++)for(int S=0;S<=U;S++){
        xv[i][j][S] = 1; 
        int all = __builtin_popcount(S) + j,num = i-1;
        for(int r=0;r<tot;r++)if(!buc[r][i]){
            int snum = num;
            for(int y=i+1;y<=n;y++)if(buc[r][y] && (S>>(buc[r][y]-1)&1))snum++;
            xv[i][j][S] = 1ll*xv[i][j][S]*max(0,all-snum)%mod;
        }
    }
    for(int i=0;i<=n;i++)pw[i] = qpow(i,m-tot);
    //

    f[0][0][0] = 1;  
    for(int i=1;i<=n;i++){
        memset(g,0,sizeof g);
        for(int j=0;j<=lim;j++){
            for(int S=0;S<=U;S++){
                int w = f[i-1][j][S]; if(!w)continue;
                int R = U^S;
                for(int T=R;;T=(T-1)&R){ 
                    int now = w;
                    for(int x=0;x<cnt;x++)if(T>>x&1){
                        if(val[x] < i){now = 0; break;}
                    }
                    if(!now)continue;
                    add(g[j][S|T],now);
                    if(!T)break;
                }
            }
        }
        for(int j=0;j<=lim;j++){
            for(int S=0;S<=U;S++){
                int w = g[j][S]; if(!w)continue;
                for(int k=0;j+k<=lim;k++){ //有k个额外列    
                    int now = 1ll*w*rfac[k]%mod*xv[i][j+k][S]%mod;
                    int all = __builtin_popcount(S) + (j+k),num = i-1;
                    //剩下m-tot行的系数是平凡的
                    int w = max(0,all-num);
                    now = 1ll*now*pw[w]%mod;

                    add(f[i][j+k][S],now);
                }
            }
        }
    }
    int ans = f[n][lim][U];
    ans = 1ll*ans*fac[lim]%mod;
    cout<<ans<<endl;
    return 0;
}