#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using i128 = __int128;
constexpr int maxn = 53;
constexpr int maxm = 10;
constexpr int mod = 998244353;
i64 qp(i64 a, i64 b)
{
    i64 c = 1;
    for (; b; b>>=1, a=a*a%mod)
        if (b & 1) c=c*a%mod;
    return c;
}
i64 c[maxn][maxn];
i64 bin[2][1 << maxm][maxn];
i128 t[maxn];
i64 pr[maxn];
int x[maxm], y[maxm], w[maxm];
int mn[1 << maxm], pc[1 << maxm], ov[maxm], ok[maxm];
void upd(i64& x, i64 y)
{
    x += y;
    if (x >= mod) x -= mod;
}
int main()
{
    c[0][0] = 1;
    for (int i=1;i<maxn;++i)
    {
        c[i][0] = 1;
        for (int j=1;j<=i;++j) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
    }
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n, m, q;
    cin >> n >> m >> q;
    for (int i=0;i<q;++i) cin >> x[i] >> y[i] >> w[i];
    vector<int> h(y, y + q), sp(x, x + q);
    sort(h.begin(), h.end());
    h.erase(unique(h.begin(), h.end()), h.end());
    int p = h.size();
    for (int i=0;i<q;++i) y[i] = lower_bound(h.begin(), h.end(), y[i]) - h.begin();
    sort(sp.begin(), sp.end());
    sp.erase(unique(sp.begin(), sp.end()), sp.end());
    for (int i=0;i<q;++i) x[i] = lower_bound(sp.begin(), sp.end(), x[i]) - sp.begin();
    for (int i=1;i<(1<<p);++i)
    {
        pc[i] = __builtin_popcount(i);
        if (pc[i] == 1)
        {
            mn[i] = 0x3f3f3f3f;
            for (int j=0;j<q;++j)
                if (i >> y[j] & 1) mn[i] = min(mn[i], w[j]);
        }
    }
    auto *f = bin[0], *g = bin[1];
    f[0][0] = 1;
    for (int i=0;i<=n;++i) pr[i] = qp(i, m - sp.size());
    for (int i=0;i<n;++i)
    {
        swap(f, g);
        for (int t=1;t<(1<<p);t<<=1)
            if (i < mn[t])
                for (int x=0;x<(1<<p);++x) if (~x & t)
                    for (int j=i;j<=n-pc[t];++j)
                        upd(g[x | t][j + pc[t]], g[x][j]);
        for (int s=0;s<(1<<p);++s)
        {
            memset(t, 0, sizeof(t));
            for (int j=i;j<=n;++j) if (g[s][j])
            {
                int l = n - p - j + pc[s];
                for (int k=0;k<=n-j&&k<=l;++k) t[j + k] += g[s][j] * c[l][k];
            }
            memset(ov, 0, sizeof(ov));
            memset(ok, 0, sizeof(ok));
            for (int j=0;j<q;++j)
                if (s >> y[j] & 1)
                {
                    if (w[j] == i + 1) ok[x[j]] = 1;
                    else if (w[j] > i + 1) ++ov[x[j]];
                }
            for (int j=i+1;j<=n;++j)
            {
                i64& v = f[s][j];
                v = t[j] % mod * pr[j - i] % mod;
                for (int k=0;k<sp.size();++k) v = ok[k] ? v : v * (j - i - ov[k]) % mod;
            }
        }
    }
    cout << f[(1 << p) - 1][n] << '\n';
    return 0;
}