#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll mod = 998244353;

int x[15], y[15], w[15], b[15], c[1024], mn[15];
int a[15][15], occ[15][55], bg[15][55];
ll f[55][1024], mi[55], fac[55], ifac[55];

ll fpow(ll a, ll b)
{
    ll ans = 1;
    while (b)
    {
        if (b & 1) ans = ans * a % mod;
        a = a * a % mod; b >>= 1;
    }
    return ans;
}

int main()
{
    ios::sync_with_stdio(false), cin.tie(0);

    int n, m, q;
    cin >> n >> m >> q;
    for (int i = 1; i <= q; i++)
    {
        cin >> x[i] >> y[i] >> w[i];
        b[i] = x[i];
    }
    fac[0] = 1; for (int i = 1; i <= n; i++) fac[i] = fac[i - 1] * i % mod;
    ifac[n] = fpow(fac[n], mod - 2); for (int i = n; i; i--) ifac[i - 1] = ifac[i] * i % mod;
    sort(b + 1, b + q + 1, [&](int x, int y) { return x < y; });
    int ln = unique(b + 1, b + q + 1) - b - 1, t = m - ln;
    for (int i = 1; i <= q; i++) x[i] = lower_bound(b + 1, b + ln + 1, x[i]) - b;
    for (int i = 1; i <= q; i++) b[i] = y[i];
    sort(b + 1, b + q + 1, [&](int x, int y) { return x < y; });
    int k = unique(b + 1, b + q + 1) - b - 1;
    for (int i = 0; i < k; i++) mn[i] = n + 1;
    for (int i = 1; i <= q; i++)
    {
        y[i] = lower_bound(b + 1, b + k + 1, y[i]) - b - 1;
        a[x[i]][y[i]] = w[i];
        if (occ[x[i]][w[i]]) return cout << "0", 0;
        else occ[x[i]][w[i]] = 1;
        mn[y[i]] = min(mn[y[i]], w[i]);
        for (int j = 1; j <= w[i]; j++) bg[x[i]][j] |= (1 << y[i]);
    }

    int K = 1 << k; f[0][0] = 1;
    for (int i = 1; i <= n; i++) mi[i] = fpow(i, t);
    for (int s = 1; s < K; s++) c[s] = c[s ^ (s & -s)] + 1;
    for (int i = 1; i <= n; i++)
    {
        for (int s = 0; s < K; s++)
            for (int l = n - k; l >= 0 && l >= i - c[s] - 1; l--)
                for (int j = l - 1; j >= i - c[s] - 1 && j >= 0; j--)
                    (f[l][s] += f[j][s] * ifac[l - j]) %= mod;
                
        for (int j = 0; j <= n - k; j++)
            for (int l = 0; l < k; l++)
                if (mn[l] >= i)
                    for (int s = 0; s < K; s++)
                        if ((s >> l) & 1)
                        {
                            f[j][s] += f[j][s ^ (1 << l)];
                            if (f[j][s] >= mod) f[j][s] -= mod;
                        }
        
        for (int j = 0; j <= n - k; j++)
            for (int s = 0; s < K; s++)
            {
                if (j + c[s] < i) { f[j][s] = 0; continue; }
                (f[j][s] *= mi[j + c[s] - i + 1]) %= mod;
                for (int l = 1; l <= ln; l++)
                {
                    if (occ[l][i]) continue;
                    if (j + c[s] - i + 1 <= c[s & bg[l][i]]) { f[j][s] = 0; break; }
                    else (f[j][s] *= (j + c[s] - i + 1 - c[s & bg[l][i]])) %= mod;
                }
            }
    }
    cout << f[n - k][K - 1] * fac[n - k] % mod;
    return 0;
}