#include<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define pii pair<ll,ll>
#define rep(i,a,b) for(ll i=(a);i<=(b);++i)
#define per(i,a,b) for(ll i=(a);i>=(b);--i)
using namespace std;
bool Mbe;
ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void write(ll x){
    if(x<0)putchar('-'),x=-x;
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
const ll N=55,Mod=998244353;
ll n,m,q;
ll X[12],Y[12],W[12],w[12][12],tx[12],ty[12],totx,toty;
//dp[i][j][S] 表示目前填完了值域 [1,i]，还有 j 列没有填过，目前关键列填了 S 中的列
ll dp[N][N][(1<<10)+5],mn[12],pc[(1<<10)+5],C[N][N],tmp[N],cnt[N],ok[N];
ll pw(ll x,ll p){
    ll res=1;
    while(p){
        if(p&1)res=res*x%Mod;
        x=x*x%Mod,p>>=1;
    }
    return res;
}
bool Med;
int main(){
    cerr<<fabs(&Med-&Mbe)/1048576.0<<"MB\n";
    n=read(),m=read(),q=read();
    rep(i,0,n){
        C[i][0]=1;
        rep(j,1,i)C[i][j]=(C[i-1][j]+C[i-1][j-1])%Mod;
    }
    rep(i,1,q)X[i]=read(),Y[i]=read(),W[i]=read();
    rep(i,1,q)tx[i]=X[i],ty[i]=Y[i];
    sort(tx+1,tx+q+1),sort(ty+1,ty+q+1);
    totx=unique(tx+1,tx+q+1)-tx-1,toty=unique(ty+1,ty+q+1)-ty-1;
    rep(i,1,q)X[i]=lower_bound(tx+1,tx+totx+1,X[i])-tx,Y[i]=lower_bound(ty+1,ty+toty+1,Y[i])-ty;
    rep(i,1,q)w[X[i]][Y[i]]=W[i];
    rep(i,1,(1<<q)-1)pc[i]=pc[i^(i&(-i))]+1;
    rep(i,1,toty){
        mn[i]=1e9;
        rep(j,1,q){
            if(i==Y[j])mn[i]=min(mn[i],W[j]);
        }
    }
    dp[0][0][0]=1;
    rep(i,0,n-1){
        rep(j,1,toty){
            if(i<mn[j]){
                rep(p,i,n-1){
                    rep(k,0,(1<<toty)-1){
                        if((k>>(j-1))&1)continue;
                        if(!dp[i][p][k])continue;
                        dp[i][p+1][k|(1<<(j-1))]=(dp[i][p+1][k|(1<<(j-1))]+dp[i][p][k])%Mod;
                    }
                }
            }
        }
        rep(j,0,(1<<toty)-1){
            memset(tmp,0,sizeof(tmp));
            rep(k,i,n){
                if(!dp[i][k][j])continue;
                ll cnt=n-toty+pc[j]-k;
                rep(p,0,min(n-k,cnt))tmp[k+p]=(tmp[k+p]+dp[i][k][j]*C[cnt][p])%Mod;
            }
            memset(cnt,0,sizeof(cnt)),memset(ok,0,sizeof(ok));
            rep(k,1,q){
                if((j>>(Y[k]-1))&1){
                    if(W[k]==i+1)ok[X[k]]=1;
                    else if(W[k]>i+1)cnt[X[k]]++;
                }
            }
            rep(k,i+1,n){
                dp[i+1][k][j]=tmp[k]*pw(k-i,m-totx)%Mod;
                rep(p,1,totx){
                    if(!ok[p])dp[i+1][k][j]=dp[i+1][k][j]*(k-i-cnt[p])%Mod;
                }
            }
        }
    }
    write(dp[n][n][(1<<toty)-1]);
    cerr<<"\n"<<clock()*1.0/CLOCKS_PER_SEC*1000<<"ms\n";
    return 0;
}