/* Problem URL: https://codeforces.com/group/YgJmumGtHD/contest/105936/problem/F */ #include using namespace std; #define V vector #define rmin(a, b) a = min(a, b) #define rmax(a, b) a = max(a, b) #define rep(i, lim) for (int i = 0; i < (lim); i++) #define nrep(i, s, lim) for (int i = s; i < (lim); i++) #define repv(i, v) for (auto &i : (v)) #define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; } #define sortv(v) sort(v.begin(), v.end()) #define all(v) (v).begin(), (v).end() using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using ll = long long; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; template auto operator<<(ostream &os, const vector &vec)->ostream& { os << vec[0]; for (size_t i = 1; i < vec.size(); i++) { os << ' ' << vec[i]; } os << '\n'; return os; } template auto operator>>(istream &is, vector &vec)->istream& { for (auto &i : vec) { is >> i; } return is; } template auto operator<<(ostream &os, const vector> &vec)->ostream& { for (auto &i : vec) { os << i[0]; for (size_t j = 1; j < i.size(); j++) { os << ' ' << i[j]; } os << '\n'; } return os; } template auto operator>>(istream &is, vector> &vec)->istream& { for (auto &i : vec) { for (auto &j : i) { is >> j; } } return is; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n, m, k; cin >> n >> m >> k; V fds(n); cin >> fds; ll valids = 0; int ri = -1; int rj = -1; rep(i, n) { rep(j, m) { if (fds[i][j] == 'R') { ri = i; rj = j; continue; } if (fds[i][j] == '.') { valids++; } } } ll inf = INT64_MAX >> 1; vl discount(n * m + 1, 0); ll minimal_cheese = inf; ll maximal = 0; auto bfs = [&](int i, int j) { vvl dis(n, vl(m, inf)); dis[i][j] = 0; queue> q; q.emplace(i, j); while (!q.empty()) { auto [i, j] = q.front(); q.pop(); rmax(maximal, dis[i][j]); if (fds[i][j] == 'Q') { rmin(minimal_cheese, dis[i][j]); } else { discount[dis[i][j]]++; } int add[][2] = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}}; repv(k, add) { int id = i + k[0]; int jd = j + k[1]; if (id >= 0 && id < n && jd >= 0 && jd < m && fds[id][jd] != '#' && dis[id][jd] > dis[i][j] + 1) { dis[id][jd] = dis[i][j] + 1; q.emplace(id, jd); } } } }; bfs(ri, rj); vl suf(n * m + 1); for (int i = n * m - 1; i >= 0; i--) { suf[i] = suf[i + 1] + discount[i]; } const ll mod = 998244353; ll divs = valids; nrep(i, 1, k) { divs *= (valids - i); divs %= mod; } vl fact(n * m + 1); fact[0] = 1; nrep(i, 1, n * m + 1) { fact[i] = fact[i - 1] * i; fact[i] %= mod; } auto fastpow = [&](ll a, ll b) { ll ans = 1; ll fds = a; rep(i, 31) { if ((b >> i) & 1) { ans *= fds; ans %= mod; } fds *= fds; fds %= mod; } return ans; }; auto comb = [&](ll a, ll k) { return (fact[a] * fastpow((fact[k] * fact[a - k]) % mod, mod - 2)) % mod; }; auto perm = [&](ll a, ll k) { return (fact[a] * fastpow(fact[a - k], mod - 2)) % mod; }; ll ans = 0; for (ll i = 1; i <= maximal && i < minimal_cheese; i++) { if (suf[i] < k) { break; } if (suf[i + 1] < k) { ans += perm(suf[i], k) * i; ans %= mod; break; } // ans += ((comb(suf[i], k) - comb(suf[i + 1], k)) % mod + mod) % mod * i; ans += ((perm(suf[i], k) - perm(suf[i + 1], k)) % mod + mod) % mod * i; ans %= mod; } if (minimal_cheese != inf && suf[minimal_cheese] >= k) { ans += perm(suf[minimal_cheese], k) * minimal_cheese; ans %= mod; } cerr << ans << '\n'; cout << (ans * fastpow(divs, mod - 2)) % mod << '\n'; }