#include <bits/stdc++.h>

#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 SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T>inline void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T>inline void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

template <int P>
class mod_int {
  using Z = mod_int;

private:
  static int mo(int x) { return x < 0 ? x + P : x; }

public:
  int x;
  int val() const { return x; }
  mod_int() : x(0) {}
  template <class T>
  mod_int(const T &x_) : x(x_ >= 0 && x_ < P ? static_cast<int>(x_) : mo(static_cast<int>(x_ % P))) {}
  bool operator==(const Z &rhs) const { return x == rhs.x; }
  bool operator!=(const Z &rhs) const { return x != rhs.x; }
  Z operator-() const { return Z(x ? P - x : 0); }
  Z pow(long long k) const {
    Z res = 1, t = *this;
    while (k) {
      if (k & 1) res *= t;
      if (k >>= 1) t *= t;
    }
    return res;
  }
  Z &operator++() {
    x < P - 1 ? ++x : x = 0;
    return *this;
  }
  Z &operator--() {
    x ? --x : x = P - 1;
    return *this;
  }
  Z operator++(int) {
    Z ret = x;
    x < P - 1 ? ++x : x = 0;
    return ret;
  }
  Z operator--(int) {
    Z ret = x;
    x ? --x : x = P - 1;
    return ret;
  }
  Z inv() const { return pow(P - 2); }
  Z &operator+=(const Z &rhs) {
    (x += rhs.x) >= P && (x -= P);
    return *this;
  }
  Z &operator-=(const Z &rhs) {
    (x -= rhs.x) < 0 && (x += P);
    return *this;
  }
  Z &operator*=(const Z &rhs) {
    x = 1ULL * x * rhs.x % P;
    return *this;
  }
  Z &operator/=(const Z &rhs) { return *this *= rhs.inv(); }
#define setO(T, o)                                 \
  friend T operator o(const Z &lhs, const Z &rhs) {\
    Z res = lhs;                                   \
    return res o## = rhs;                          \
  }
  setO(Z, +) setO(Z, -) setO(Z, *) setO(Z, /)
#undef setO
};
const int P = 998244353;
using Z = mod_int<P>;

const int maxn = 55;

int n, m, q, tot, ln, a[maxn][maxn], vis[maxn], id[maxn], pos[maxn], popc[1 << 10];
int cnt[maxn][maxn][1 << 10];
// 第 i 行，S 集合的特殊列内有多少个 <=j 的数
// 第 i 行，S 集合内有多少个数是被钦定的
Z fac[maxn], ivf[maxn], f[maxn][maxn][1 << 10], pw[maxn], prd[maxn][maxn], mprd[maxn][maxn];
map<int, int> mp;

Z binom(int x, int y) {
  if (x < 0 || y < 0 || x < y) return 0;
  return fac[x] * ivf[y] * ivf[x - y];
}

int main() {
  fac[0] = 1;
  rep (i, 1, maxn - 1) fac[i] = fac[i - 1] * i;
  ivf[maxn - 1] = fac[maxn - 1].inv();
  per (i, maxn - 1, 1) ivf[i - 1] = ivf[i] * i;
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  cin >> n >> m >> q;
  rep (i, 1, q) {
    int x, y, w;
    cin >> x >> y >> w;
    if (!mp.count(x)) mp[x] = ++ln;
    a[mp[x]][y] = n - w + 1, vis[y] = 1;
  }
  rep (i, 1, n) if (vis[i]) pos[++tot] = i, id[i] = tot;
  int U = (1 << tot) - 1;
  rep (i, 1, n) pw[i] = Z(i).pow(m - ln);
  rep (i, 1, (1 << tot) - 1) popc[i] = __builtin_popcount(i);
  rep (i, 1, ln) {
    rep (S, 0, (1 << tot) - 1) {
      rep (j, 1, tot) if (a[i][pos[j]] && (S >> (j - 1) & 1)) cnt[i][a[i][pos[j]]][S]++;
      rep (j, 1, n) cnt[i][j][S] += cnt[i][j - 1][S];
    }
  }
  rep (l, 1, n) {
    prd[l][l - 1] = 1;
    rep (r, l, n) prd[l][r] = prd[l][r - 1] * r;
  }
  rep (l, 1, n) rep (r, 1, n) mprd[l][r] = prd[l][r].pow(m - ln);
  f[0][0][0] = 1;
  rep (i, 1, n) {
    rep (S, 0, (1 << tot) - 1) rep (j, 0, n - tot) {
      rep (k, 0, j) if (f[i - 1][j - k][S].val()) {
        Z ways = binom(n - tot - j + k, k);
        if (i - (j - k + popc[S] + k - 1) < 0) continue;
        int L = i - (j - k + popc[S] + k - 1), R = i - (j - k + popc[S]);
        if (L >= 0) ways *= mprd[L][R];
        rep (o, 1, ln) {
          int cur = j - k + popc[S] + cnt[o][i][U ^ S];
          int L = i - cur - k + 1, R = i - cur;
          if (L >= 0) ways *= prd[L][R];
          if (!ways.val()) break;
        }
        if (ways.val()) f[i][j][S] += f[i - 1][j - k][S] * ways;
      }
    }
    rep (d, 1, tot) {
      rep (j, 0, n - tot) rep (S, 0, (1 << tot) - 1) {
        if ((S >> (d - 1) & 1) || !f[i][j][S].val()) continue;
        Z ways = 1;
        if (i - (j + popc[S]) < 0) continue;
        ways *= pw[i - (j + popc[S])];
        rep (o, 1, ln) {
          if (a[o][pos[d]] > i) ways = 0;
          else if (!a[o][pos[d]]) ways *= (i - (j + popc[S] + cnt[o][i][U ^ S]));
          if (!ways.val()) break;
        }
        if (ways.val()) f[i][j][S ^ (1 << (d - 1))] += f[i][j][S] * ways;
      }
    }
  }
  cout << f[n][n - tot][U].val() << '\n';
}