// yukicoder/1836/main.cpp // author: @___Johniel // github: https://github.com/johniel/ #include #define each(i, c) for (auto& i : c) #define unless(cond) if (!(cond)) using namespace std; template ostream& operator << (ostream& os, pair p) { os << "(" << p.first << "," << p.second << ")"; return os; } template istream& operator >> (istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator << (ostream& os, vector v) { os << "("; for (auto& i: v) os << i << ","; os << ")"; return os; } template istream& operator >> (istream& is, vector& v) { for (auto& i: v) is >> i; return is; } template ostream& operator << (ostream& os, set s) { os << "#{"; for (auto& i: s) os << i << ","; os << "}"; return os; } template ostream& operator << (ostream& os, map m) { os << "{"; for (auto& i: m) os << i << ","; os << "}"; return os; } template inline T setmax(T& a, T b) { return a = std::max(a, b); } template inline T setmin(T& a, T b) { return a = std::min(a, b); } using lli = long long int; using ull = unsigned long long; using point = complex; using str = string; template using vec = vector; constexpr array di({0, 1, -1, 0, 1, -1, 1, -1}); constexpr array dj({1, 0, 0, -1, 1, -1, -1, 1}); constexpr lli mod = 998244353; const int N = 2 * 1e5 + 3; namespace math { lli fact[N], finv[N], inv[N]; void init() { fact[0] = fact[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < N; i++){ fact[i] = fact[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } lli mod_comb(int n, int k) { assert(n < N && k < N); if (n < k) return 0; if (n < 0 || k < 0) return 0; return fact[n] * (finv[k] * finv[n - k] % mod) % mod; } inline lli nCk(int n, int k) { return mod_comb(n, k); } // n個の箱にm個の何かを分配する場合の数 inline lli nHm(int n, int m) { return nCk(n + m - 1, m); } }; namespace math { lli extgcd(lli a, lli b, lli& x, lli& y) { lli g = a; x = 1; y = 0; if (b != 0) { g = extgcd(b, a % b, y, x); y -= (a / b) * x; } return g; } lli mod_inverse(lli a, lli m) { lli x, y; extgcd(a, m, x, y); return (m + x % m) % m; } lli mod_pow(lli n, lli p) { if (p == 0) return 1; if (p == 1) return n; lli m = mod_pow(n, p / 2); m *= m; m %= mod; if (p % 2) m = (m * n) % mod; return m; } }; int main(int argc, char *argv[]) { ios_base::sync_with_stdio(0); cin.tie(0); cout.setf(ios_base::fixed); cout.precision(15); math::init(); int h, w, m; while (cin >> h >> w >> m) { lli z = 0; for (int i = 0; i < m; ++i) { lli a = math::mod_pow(m - i, h) - math::mod_pow(m - i - 1, h) + mod; lli b = math::mod_pow(m - i, w) - math::mod_pow(m - i - 1, w) + mod; (z += a * b % mod) %= mod; } cout << z << endl; } return 0; }