#include<iostream>
#include<cstdio>
#include<vector>
#include<map>
#define N 50
#define M 10
#define mod 998244353
using namespace std;
int read()
{
	char c=0;
	int sum=0;
	while (c<'0'||c>'9') c=getchar();
	while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
	return sum;
}
void Adder(int &x,int d)
{
	x=x+d>=mod?x+d-mod:x+d;
	return;
}
void Adder2(int &x,int d)
{
	x=x+d<0?x+d+mod:x+d;
	return;
}
int MD(int x)
{
	return x>=mod?x-mod:x;
}
int MD2(int x)
{
	return x<0?x+mod:x;
}
int fast_pow(int a,int b)
{
	int res=1,mul=a;
	while (b)
	{
		if (b&1) res=1ll*res*mul%mod;
		mul=1ll*mul*mul%mod,b>>=1;
	}
	return res;
}
struct reads
{
	int num,data;
};
int n,m,q,leng,ans,tong[N+1],length,cnt[N+1],delta[N+1][N+1],fac[N+1],invfac[N+1],dp[N+1][1<<M][N+1][N+1],F[1<<M][N+1][N+1],G[1<<M][N+1];
bool used[N+1];
vector<reads>v[N+1];
vector<reads>v2[N+1];
map<int,int>p;
map<int,int>vis[N+1];
int main()
{
	bool op;
	int x,y,w,res;
	fac[0]=1;
	for (int i=1;i<=N;++i) fac[i]=1ll*fac[i-1]*i%mod;
	invfac[N]=fast_pow(fac[N],mod-2);
	for (int i=N-1;i>=0;--i) invfac[i]=1ll*invfac[i+1]*(i+1)%mod;
	n=read(),m=read(),q=read();
	while (q--)
	{
		x=read(),y=read(),w=read();
		if (!vis[y][x])
		{
			if (!p[x]) p[x]=++leng;
			v[p[x]].push_back((reads){y,w}),v2[y].push_back((reads){p[x],w}),vis[y][x]=1;
		}
	}
	for (int i=1;i<=leng;++i)
	{
		for (int j=0;j<v[i].size();++j)
			for (int k=j+1;k<v[i].size();++k)
				if (v[i][j].data==v[i][k].data)
				{
					puts("0");
					return 0;
				}
		for (int j=1;j<=n;++j) delta[i][j]=1;
		for (int j=0;j<v[i].size();++j) delta[i][v[i][j].data]=0;
		for (int j=n-1;j>=1;--j) delta[i][j]+=delta[i][j+1];
	}
	for (int i=1;i<=n;++i)
		if (!v2[i].empty())
			tong[++length]=i;
	dp[n][0][0][0]=1;
	for (int i=n;i>=1;--i)
	{
		for (int j=0;j<(1<<length);++j)
			for (int k=0;k<=n-length;++k)
			{
				for (int t=1;t<=length;++t) F[j][k][t]=0;
				G[j][k]=0;
			}
		for (int j=0;j<(1<<length);++j)
			for (int k=0;k<=n-length;++k)
				if (__builtin_popcount(j)+k<n-i+1)
				{
					for (int t=1;t<=length;++t)
						if (!((j>>(t-1))&1))
						{
							res=fast_pow((n-i+1)-__builtin_popcount(j)-k,m-leng),op=1;
							for (int z=1;z<=leng;++z) used[z]=0;
							for (int z=0;z<v2[tong[t]].size();++z) used[v2[tong[t]][z].num]=1,op&=(v2[tong[t]][z].data>=i);
							if (!op) continue;
							for (int w=1;w<=leng;++w) cnt[w]=delta[w][i]-(__builtin_popcount(j)+k);
							for (int w=1;w<=length;++w)
								if ((j>>(w-1))&1)
								{
									for (int z=0;z<v2[tong[w]].size();++z) cnt[v2[tong[w]][z].num]++;
								}
							for (int w=1;w<=leng;++w)
								if (!used[w])
									res=1ll*res*cnt[w]%mod;
							F[j][k][t]=res;
						}
					res=fast_pow((n-i+1)-__builtin_popcount(j)-k,m-leng);
					for (int w=1;w<=leng;++w) cnt[w]=delta[w][i]-(__builtin_popcount(j)+k);
					for (int w=1;w<=length;++w)
						if ((j>>(w-1))&1)
						{
							for (int z=0;z<v2[tong[w]].size();++z) cnt[v2[tong[w]][z].num]++;
						}
					for (int w=1;w<=leng;++w) res=1ll*res*cnt[w]%mod;
					G[j][k]=res;
				}
		for (int j=0;j<(1<<length);++j)
			for (int k=0;k<=n-length;++k)
				for (int t=0;t<=n;++t)
					if (dp[i][j][k][t])
					{
						if (i!=1) Adder(dp[i-1][j][k][0],1ll*dp[i][j][k][t]*invfac[t]%mod);
						for (int w=1;w<=length;++w)
							if (!((j>>(w-1))&1))
								Adder(dp[i][j|(1<<(w-1))][k][t+1],1ll*dp[i][j][k][t]*F[j][k][w]%mod);
						if (k+1<=n-length) Adder(dp[i][j][k+1][t+1],1ll*dp[i][j][k][t]*G[j][k]%mod*(n-length-k)%mod);
					}
	}
	for (int i=0;i<=n;++i) Adder(ans,1ll*dp[1][(1<<length)-1][n-length][i]*invfac[i]%mod);
	printf("%d\n",ans);
	return 0;
}