#include <cassert>
#include <cstdio>
#include <cstring>
#include <map>
using namespace std;
const int P = 998244353;
typedef long long ll;
int read() {
    char c = getchar();
    int x = 0;
    while (c < 48 or c > 57)
        c = getchar();
    do
        x = x * 10 + (c ^ 48), c = getchar();
    while (c >= 48 and c <= 57);
    return x;
}
const int N = 53, S = 1 << 10, T = 10;
inline void inc(int &x, int v) {
    if ((x += v) >= P)
        x -= P;
}
map<int, int> id;
int n, m, q, cnt, rk;
int f[S][N], g[S][N], h[S];
int fac[N], fiv[N];
int pfac[N], pfiv[N];
int mp[N];
int qp(int a, int b = P - 2) {
    int res = 1;
    while (b) {
        if (b & 1)
            res = (ll)res * a % P;
        a = (ll)a * a % P;
        b >>= 1;
    }
    return res;
}
inline int C(int x, int y) {
    return (ll)fac[x] * fiv[y] % P * fiv[x - y] % P;
}
int w[T][T], msk2[T];
int main() {
    n = read(), m = read(), q = read();
    for (int i = 1; i <= n; ++i)
        mp[i] = -1;
    for (int i = 1; i <= q; ++i) {
        int x = read(), y = read();
        if (id.find(x) == id.end())
            id[x] = cnt++;
        if (mp[y] < 0)
            mp[y] = rk++;
        x = id[x], y = mp[y];
        w[x][y] = read();
    }
    fac[0] = 1;
    for (int i = 1; i <= n; ++i)
        fac[i] = (ll)fac[i - 1] * i % P;
    fiv[n] = qp(fac[n]);
    for (int i = n; i; --i)
        fiv[i - 1] = (ll)fiv[i] * i % P;
    for (int i = 0; i <= n; ++i) {
        pfac[i] = qp(fac[i], m - cnt);
        pfiv[i] = qp(fiv[i], m - cnt);
    }
    f[0][0] = 1;
    for (int i = n; i; --i) {
        int msk1 = 0;
        for (int u = 0; u < cnt; ++u) {
            msk2[u] = 0;
            for (int v = 0; v < rk; ++v)
                if (w[u][v]) {
                    if (w[u][v] < i)
                        msk1 |= (1 << v);
                    else
                        msk2[u] |= (1 << v);
                }
        }
        for (int s = 0; s < (1 << rk); ++s)
            for (int x = 0, c = __builtin_popcount(s);
                 x <= n - rk and c <= n - i; ++x, ++c) {
                f[s][x] = (ll)f[s][x] * pfac[n - i + 1 - c] % P;
                for (int u = 0; u < cnt; ++u) {
                    int cur = n - i + 1 - c;
                    cur -= __builtin_popcount(~s & msk2[u]);
                    if (cur >= 0)
                        f[s][x] = (ll)f[s][x] * fac[cur] % P;
                    else
                        f[s][x] = 0;
                }
            }
        for (int x = 0; x <= n - i; ++x) {
            for (int s = 0; s < (1 << rk); ++s)
                h[s] = f[s][x];
            for (int p = 0; p < rk; ++p)
                if (~msk1 >> p & 1)
                    for (int e = 0; e < (1 << rk); e += (2 << p))
                        for (int t = e; t < (e | (1 << p)); ++t)
                            inc(h[t | (1 << p)], h[t]);
            for (int s = 0; s < (1 << rk); ++s)
                for (int y = x, c = __builtin_popcount(s) + x;
                     y <= n - rk and c <= n - i + 1; ++y, ++c)
                    g[s][y] = (g[s][y] + (ll)h[s] * C(n - rk - x, y - x)) % P;
        }
        for (int s = 0; s < (1 << rk); ++s)
            for (int x = 0, c = __builtin_popcount(s);
                 x <= n - rk and c <= n - i + 1; ++x, ++c) {
                f[s][x] = (ll)g[s][x] * pfiv[n - i + 1 - c] % P;
                g[s][x] = 0;
                for (int u = 0; u < cnt; ++u) {
                    int cur = n - i + 1 - c;
                    cur -= __builtin_popcount(~s & msk2[u]);
                    if (cur >= 0)
                        f[s][x] = (ll)f[s][x] * fiv[cur] % P;
                    else
                        f[s][x] = 0;
                }
            }
    }
    printf("%d\n", f[(1 << rk) - 1][n - rk]);
    return 0;
}