//A tree without skin will surely die.
//A man without face will be alive.
#include<bits/stdc++.h>
using namespace std;
#define rep(i,j,k) for(int i=j;i<=k;++i)
#define per(i,j,k) for(int i=j;i>=k;--i)
#define add(x,y) (x=((x+y>=mod)?(x+y-mod):(x+y)))
int const N=60,mod=998244353;
int n,m,q,ctx,cty,fac[N],inv[N],mi[1<<10],a[11][11],pop[1<<10],dp[N][N][1<<10],f[N][1<<10],F[N][1<<10],C[N][N],num[1<<10][11][N];
unordered_map<int,int>H,W;
inline int qpow(int a,int b){int res=1;while (b){if (b&1) res=1ll*res*a%mod;a=1ll*a*a%mod,b>>=1;}return res;}
inline void solve(){
	cin>>n>>m>>q;
	rep(i,0,n){
		C[i][0]=C[i][i]=1;
		rep(j,1,i-1) C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
	}
	fac[0]=1;
	rep(i,1,n) fac[i]=1ll*fac[i-1]*i%mod;
	inv[n]=qpow(fac[n],mod-2);
	per(i,n-1,0) inv[i]=1ll*inv[i+1]*(i+1)%mod;
	while (q--){
		int x,y,w;cin>>x>>y>>w;
		if (!H.count(x)) H[x]=++ctx;
		if (!W.count(y)) W[y]=++cty;
		x=H[x],y=W[y],a[x][y]=w;
	}
	rep(S,1,(1<<cty)-1){
		pop[S]=pop[S-(S&(-S))]+1;
		rep(l,1,ctx) rep(i,1,n) rep(j,1,cty)
			if ((S>>(j-1)&1) && a[l][j]>=i) ++num[S][l][i];
	}
	dp[0][0][0]=1;
	memset(mi,0x3f,sizeof(mi));
	rep(S,0,(1<<cty)-1) rep(x,1,ctx) rep(y,1,cty)
		if (!(S>>(y-1)&1) && a[x][y]) mi[S]=min(mi[S],a[x][y]);
	rep(i,1,n){
		memset(F,0,sizeof(F));
		int la=i-1;
		rep(j,i,n){
			rep(k,la,j) rep(T,0,(1<<cty)-1){
				int rg=1ll*dp[i-1][k][T]*qpow(inv[k-i+1],m-ctx)%mod;
				rep(l,1,ctx)
					if (k-i+1-num[T][l][i]<0) rg=0;
					else rg=1ll*rg*inv[k-i+1-num[T][l][i]]%mod;
				add(F[k-pop[T]+8][T],rg);
			}
			la=j+1,memcpy(f,F,sizeof(f));
			rep(i,0,j+8) rep(d,0,cty-1) rep(S,0,(1<<cty)-1)
				if (S>>d&1) add(f[i][S],f[i][S^(1<<d)]);
			rep(S,0,(1<<cty)-1){
				if (mi[S]<=i) continue;
				int lf=qpow(fac[j-i+1],m-ctx);
				rep(l,1,ctx)
					if (j-i+1-num[S][l][i]<0){lf=0;break;}
					else lf=1ll*lf*fac[j-i+1-num[S][l][i]]%mod;
				if (!lf) continue;
				rep(pp,-8,j){
					if (j-pop[S]-pp<0) break;
					if (!f[pp+8][S]) continue;
					add(dp[i][j][S],1ll*C[n-cty-pp][j-pop[S]-pp]*f[pp+8][S]%mod);
				}
				dp[i][j][S]=1ll*dp[i][j][S]*lf%mod;
			}
		}
	}
	cout<<dp[n][n][(1<<cty)-1]<<'\n';
}
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	int t=1;
	// cin>>t;
	while (t--) solve();
	return 0;
}