#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


int N, M, Q;
vector<int> X, Y, W;

int M0, N0;
int V[11][11];

int gt[11][55];
Mint bn[55][55];
Mint dp[1 << 10][55];

int main() {
  for (; ~scanf("%d%d%d", &N, &M, &Q); ) {
    X.resize(Q);
    Y.resize(Q);
    W.resize(Q);
    for (int q = 0; q < Q; ++q) {
      scanf("%d%d%d", &X[q], &Y[q], &W[q]);
    }
    
    bool valid = true;
    {
      map<pair<int, int>, int> w;
      for (int q = 0; q < Q; ++q) w[make_pair(X[q], Y[q])] = W[q];
      for (int q = 0; q < Q; ++q) valid = valid && (w[make_pair(X[q], Y[q])] == W[q]);
    }
    Mint ans = 0;
    if (valid) {
      {
        auto xs = X;
        auto ys = Y;
        sort(xs.begin(), xs.end());
        sort(ys.begin(), ys.end());
        xs.erase(unique(xs.begin(), xs.end()), xs.end());
        ys.erase(unique(ys.begin(), ys.end()), ys.end());
        M0 = xs.size();
        N0 = ys.size();
        memset(V, 0, sizeof(V));
        for (int q = 0; q < Q; ++q) {
          X[q] = lower_bound(xs.begin(), xs.end(), X[q]) - xs.begin();
          Y[q] = lower_bound(ys.begin(), ys.end(), Y[q]) - ys.begin();
          V[X[q]][Y[q]] = W[q];
        }
      }
cerr<<"M0 = "<<M0<<", N0 = "<<N0<<", V = "<<endl;for(int x=0;x<M0;++x)pv(V[x],V[x]+N0);
      vector<int> on(M0, 0);
      vector<int> minVs(N0, N);
      memset(gt, 0, sizeof(gt));
      for (int x = 0; x < M0; ++x) for (int a = 1; a <= N; ++a) gt[x][a] = N + 1 - a;
      for (int x = 0; x < M0; ++x) for (int y = 0; y < N0; ++y) if (V[x][y]) {
        on[x] |= 1 << y;
        chmin(minVs[y], V[x][y]);
        for (int a = 1; a <= V[x][y]; ++a) --gt[x][a];
      }
      memset(bn, 0, sizeof(bn));
      for (int n = 0; n <= N; ++n) {
        bn[n][0] = bn[n][n] = 1;
        for (int k = 1; k < n; ++k) bn[n][k] = bn[n - 1][k - 1] + bn[n - 1][k];
      }
      memset(dp, 0, sizeof(dp));
      dp[0][0] = 1;
      for (int a = N; a >= 1; --a) {
        for (int y = 0; y < N0; ++y) if (minVs[y] >= a) {
          for (int h = 0; h < 1 << N0; ++h) if (!(h & 1 << y)) for (int k = 0; k <= N - N0; ++k) {
            Mint t = dp[h][k];
            if (t) {
              for (int x = 0; x < M0; ++x) if (!V[x][y]) {
                t *= (gt[x][a] - (__builtin_popcount(h & ~on[x]) + k));
              }
              t *= Mint((N + 1 - a) - (__builtin_popcount(h) + k)).pow(M - M0);
            }
            dp[h | 1 << y][k] += t;
          }
        }
// if(M<=3&&N<=3){cerr<<"HALF a = "<<a<<endl;for(int h=0;h<1<<N0;++h){cerr<<"  dp["<<h<<"] = ";pv(dp[h],dp[h]+(N-N0+1));}}
        for (int h = 0; h < 1 << N0; ++h) for (int k = N - N0; k >= 0; --k) {
          Mint t = dp[h][k];
          for (int kk = k; kk < N - N0; ) {
            for (int x = 0; x < M0; ++x) {
              t *= (gt[x][a] - (__builtin_popcount(h & ~on[x]) + kk));
            }
            t *= Mint((N + 1 - a) - (__builtin_popcount(h) + kk)).pow(M - M0);
            if (!t) break;
            ++kk;
            dp[h][kk] += t * bn[kk][k];
          }
        }
// if(M<=3&&N<=3){cerr<<"DONE a = "<<a<<endl;for(int h=0;h<1<<N0;++h){cerr<<"  dp["<<h<<"] = ";pv(dp[h],dp[h]+(N-N0+1));}}
      }
      ans = dp[(1 << N0) - 1][N - N0];
    }
    
    printf("%u\n", ans.x);
  }
  return 0;
}