#include<bits/stdc++.h>

#define ll long long
#define pi pair<int,int>
#define vi vector<int>
#define cpy(x,y,s) memcpy(x,y,sizeof(x[0])*(s))
#define mset(x,v,s) memset(x,v,sizeof(x[0])*(s))
#define all(x) begin(x),end(x)
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ary array
#define IL inline
#define eb emplace_back
#define For(i,j,k) for(int i=(j);i<=(k);i++)
#define Fol(i,k,j) for(int i=(k);i>=(j);i--)

#define mod 998244353
#define N 1100
#define M 55

using namespace std;
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0' || ch>'9')f=(ch=='-'?-1:f),ch=getchar();
    while(ch>='0' && ch<='9')x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
    return x*f;
}
void write(int x){
    if(x<0)x=-x,putchar('-');
    if(x/10)write(x/10);
    putchar(x%10+'0');
}

void debug(auto &&...x){
    ((cerr<<x<<' '),...);
    cerr<<'\n';
}

IL int pls(int x,int y){return (x+y>=mod?x+y-mod:x+y);}
IL int sub(int x,int y){return (x-y<0?x-y+mod:x-y);}
IL void Add(int &x,int y){x=pls(x,y);}
IL void Dec(int &x,int y){x=sub(x,y);}
IL int mul(int x,int y){return x*1ll*y%mod;}
IL int qp(int x,int y=mod-2){int ans=1;while(y){if(y&1)ans=mul(ans,x);x=mul(x,x);y>>=1;}return ans;}

int fac[N],ifac[N],inv[N];
IL int C(int x,int y){return mul(fac[x],mul(ifac[y],ifac[x-y]));}
IL void init(){
    fac[0]=ifac[0]=inv[0]=inv[1]=1;
    for(int i=1;i<N;i++)fac[i]=mul(fac[i-1],i);
    ifac[N-1]=qp(fac[N-1]);
    for(int i=N-2;i>=1;i--)ifac[i]=mul(ifac[i+1],i+1);
    for(int i=2;i<N;i++)inv[i]=mul((mod-mod/i),inv[mod%i]);
}

struct Node{
    int x,y,w;
    Node(int x=0,int y=0,int w=0):x(x),y(y),w(w){}
}Q[N];

int g[M][M][N],f[M][M][N],minn[N],I[M];
int c[M],d[M],pw[M],ipw[M];

unordered_map<int,int> vis,vis2;

void FWT(int *f,int L){
    for(int len=2,mid=1;len<=L;len<<=1,mid<<=1){
        for(int j=0;j<L;j+=len){
            for(int k=j;k<j+mid;k++)Add(f[k+mid],f[k]);
        }
    }
}

int main(){
    #ifdef EAST_CLOUD
    freopen("a.in","r",stdin);
    //freopen("a.out","w",stdout);
    #endif
    
    int n=read(),m=read(),q=read(),cnt=0,cnt2=0;init();
    
    For(i,1,q){
        int x=read(),y=read(),w=read();
        if(!vis[x])vis[x]=++cnt,c[cnt]=x;
        if(!vis2[y])vis2[y]=++cnt2,d[cnt2]=y,I[cnt2]=w;
        else I[vis2[y]]=min(I[vis2[y]],w);
        //debug(w);
        Q[i]=Node(x,y,w);
    }
    For(i,0,n)pw[i]=qp(fac[i],m-cnt),ipw[i]=qp(ifac[i],m-cnt);
    For(i,1,cnt){
        int id=c[i];
        Fol(j,n,1)For(S,0,(1<<cnt2)-1){
            For(k,1,q){
                if(S&(1<<(vis2[Q[k].y]-1)))continue;
                if(vis[Q[k].x]==i && Q[k].w>=j)g[i][j][S]++;
            }
        }
    }
    minn[0]=n+5;
    For(S,1,(1<<cnt2)-1){
        int lb=(S&(-S)),u=__lg(lb)+1;
        minn[S]=min(minn[S^ lb],I[u]);
        //debug(S,minn[S],I[u]);
    }
    f[n][0][0]=1;
    Fol(i,n,0){
        For(j,0,n-cnt2){
            if(i!=n){
                FWT(f[i][j],(1<<cnt2));
                For(S,0,(1<<cnt2)-1){
                    int D=n-i-j-__builtin_popcount(S);
                    if(minn[S]<i+1){f[i][j][S]=0;continue;}
                    if(D<0){f[i][j][S]=0;continue;}
                    f[i][j][S]=mul(f[i][j][S],ipw[D]);
                    For(t,1,cnt){
                        D=n-j-i-__builtin_popcount(S)-g[t][i+1][S];
                        //if(i==1 && j==0 && S==1)debug(g[t][i+1][S],D,ifac[D]);
                        if(D<0){f[i][j][S]=0;break;}
                        f[i][j][S]=mul(f[i][j][S],ifac[D]);
                    }
                }
            }
            if(i==0)continue;
            For(S,0,(1<<cnt2)-1){
                if(!f[i][j][S])continue;
                //debug(i,j,S,f[i][j][S]);
                For(k,j,n){
                    int D=n-i+1-j-__builtin_popcount(S),res=mul(pw[D],C(k,j));
                    if(D<0)continue;
                    //debug(i,j,k,S,D);
                    For(t,1,cnt){
                        int D2=n-j-__builtin_popcount(S)-i+1-g[t][i][S];
                        if(D2<0){res=0;break;}
                        res=mul(res,fac[D2]);
                        //if(i==2 && j==0 && S==0 && k==0)debug("**",t,g[t][i][S],D2,fac[D2]);
                    }
                    
                    Add(f[i-1][k][S],mul(res,f[i][j][S]));
                }
            }
        }
    }
    write(f[0][n-cnt2][(1<<cnt2)-1]);putchar('\n');
    return 0;
}