// Enjoy your stay. Code by evima #include #include #include #include #include #include #include #include #include #include #include #include using namespace atcoder; using mint = modint998244353;// modint1000000007;// modint; #include using namespace std; using ld = long double; using ll = long long; using lll = __int128; using vl = vector; using vs = vector; using LOOPVAR_TYPE = ll; #define all(x) (x).begin(), (x).end() #define sq(x) ((x) * (x)) #define sz(x) ll((x).size()) #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define rep1(i, n) rep2(i, 0, n) #define rep2(i, a, b) for(LOOPVAR_TYPE i = LOOPVAR_TYPE(a); i < LOOPVAR_TYPE(b); i++) #define rep(...) GET_MACRO(__VA_ARGS__, rep2, rep1)(__VA_ARGS__) #define eb emplace_back #define fir first #define sec second #define mp make_pair #define mt make_tuple const ld EPS = 1e-9; const ld PI = 3.14159265358979323846L; const ll INF = 1070000000LL; const ll MOD = 998244353LL;// 1000000007LL; void fast_io() { cin.tie(NULL); ios_base::sync_with_stdio(false); } ll lin() { ll x; cin >> x; return x; } string input() { string s; cin >> s; return s; } vl vin(int n) { vector v(n); rep(i, n) cin >> v[i]; return v; } template bool chmin(T& a, const T& b) { return (b < a) ? (a = b, true) : false; } template bool chmax(T& a, const T& b) { return (a < b) ? (a = b, true) : false; } template map freq(const vector& v){ map ret; for(T x: v) ++ret[x]; return ret; } template vector reversed(vector v) { reverse(all(v)); return v; } template vector sorted(vector v) { sort(all(v)); return v; } template vector sub(const vector& v, int from, int to) { vector ret; copy(&v[from], &v[to], back_inserter(ret)); return ret; } template string str(const T& x) { stringstream ss; ss << x; return ss.str(); } template array str_tuple_impl(stringstream& ss, Tuple&& t, index_sequence){ return {{ (void( ss << str(get(t)) << " " ), 0)... }}; } template string str_tuple(Tuple&& t){ stringstream ss; str_tuple_impl(ss, forward(t), make_index_sequence>::value>{}); string s = ss.str(); if(s.size() > 0) s.pop_back(); return s; } template string str(const pair& p) { return str_tuple(p); } template string str(const tuple& t) { return str_tuple(t); } template string str(const vector& v) { stringstream ss; rep(i, sz(v)) ss << v[i] << (i < sz(v) - 1 ? " " : ""); return ss.str(); } template void print1(T&& x, const string& end) { cout << str(x) << end; } void print() { print1("", "\n"); } template void print(T&& head, U&&... tail) { print1(head, " "); print(forward(tail)...); } template void eprint1(T&& x, const string& end) { cerr << str(x) << end; } void eprint() { eprint1("", "\n"); } template void eprint(T&& head, U&&... tail) { eprint1(head, " "); eprint(forward(tail)...); } template void quit(T&&... x) { print(forward(x)...); exit(0); } template void yn(bool cnd, T&& yes = "Yes", U&& no = "No") { if(cnd) print(yes); else print(no); } void zip(vl& v) { vl w = v; sort(all(w)); int n = unique(all(w)) - w.begin(); for(ll& x: v) x = lower_bound(&w[0], &w[n], x) - &w[0]; } vl zipped(vl v) { zip(v); return v; } map zipmap(vl v) { map ret; sort(all(v)); v.erase(unique(all(v)), v.end()); rep(i, sz(v)) ret[v[i]] = i; return ret; } vector fact, ifact, inv; void init_fact_ifact_inv(ll n){ fact.resize(n + 1); ifact.resize(n + 1); inv.resize(n + 1); fact[0] = 1; rep(i, n){ fact[i + 1] = fact[i] * (i + 1); } ifact[n] = fact[n].inv(); for(int i = n - 1; i >= 0; --i){ ifact[i] = ifact[i + 1] * (i + 1); } rep(i, n){ inv[i + 1] = fact[i] * ifact[i + 1]; } } const mint ncr(ll n, ll r){ return n < 0 || r < 0 || r > n ? 0 : fact[n] * ifact[r] * ifact[n - r]; } void solveOne(){ ll N, M, K; cin >> N >> M >> K; init_fact_ifact_inv(N * (N + 2)); mint ans = 0; rep(i, 1, N + 1){ rep(j, 1, N + 1){ ans += ((K + i + j) & 1 ? -1 : 1) * ncr(N, i) * ncr(N, j) * ncr(2 * N - i - j, 2 * N - K - i - j) * ncr(i * j, M); } } print(ans.val()); } int main(){ fast_io(); cout << setprecision(20); int num_tc = 1; // cin >> num_tc; rep(tc, 1, num_tc + 1){ // cout << "Case #" << tc << ": " ;// << endl; solveOne(); } }