#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef vector vl; typedef vector> vvl; typedef pair P; #define rep(i, n) for(ll i = 0; i < n; i++) #define exrep(i, a, b) for(ll i = a; i <= b; i++) #define out(x) cout << x << endl #define exout(x) printf("%.10f\n", x) #define chmax(x, y) x = max(x, y) #define chmin(x, y) x = min(x, y) #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define pb push_back #define re0 return 0 const ll mod = 998244353; const ll INF = 1e16; const ll MAX = 250010; ll fact[MAX]; // fact[i] : iの階乗のmod ll inv[MAX]; // inv[i] : iの逆数のmod ll invfact[MAX]; // invfact[i] : iの階乗の逆数のmod void init() { fact[0] = 1; inv[0] = inv[1] = 1; invfact[0] = 1; for(ll i = 1; i < MAX; i++) { fact[i] = i * fact[i-1] % mod; if(i >= 2) { inv[i] = mod - inv[mod % i] * (mod / i) % mod; } invfact[i] = invfact[i-1] * inv[i] % mod; } } // nCrをO(n)で求める。 ll Comb(ll n, ll r) { if(r < 0 || n < 0 || n < r) { return 0; } ll res = fact[n]; res = (res * invfact[r]) % mod; res = (res * invfact[n - r]) % mod; return res; } // a^n (mod.MOD)を求める。計算量はO(logn) ll modpow(ll a, ll n, ll MOD = mod) { if(n == 0) { return 1; } if(n % 2 == 1) { return a * modpow(a, n-1, MOD) % MOD; } return modpow(a, n/2, MOD) * modpow(a, n/2, MOD) % MOD; } int main() { ll n, m, k; cin >> n >> m >> k; if(n > 500) { re0; } init(); ll ans = 0; exrep(h, 0, n) { // 選んだ点を1個以上含む行の個数 ll w = 2*n - k - h; // 選んだ点を1個以上含む列の個数 ll x = 0; exrep(i, 0, h) { exrep(j, 0, w) { ll y = Comb(h, i) * Comb(w, j) % mod * Comb((h - i) * (w - j), m); if((i + j) % 2 == 0) { x += y; } else { x += mod - y; } x %= mod; } } ans += Comb(n, h) * Comb(n, w) % mod * x; ans %= mod; } out(ans); re0; }