#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T> void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T> void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

const int mod = 998244353;
const int iv2 = (mod + 1) >> 1;
const int maxn = 2000010;

int fpw(int a, int p = mod - 2) {
  int res = 1;
  while (p) {
    if (p & 1) res = 1ll * res * a % mod;
    a = 1ll * a * a % mod, p >>= 1;
  }
  return res;
}

inline void add(int &x, int y) { x += y; if (x >= mod) x -= mod; }
inline void sub(int &x, int y) { x -= y; if (x < 0) x += mod; }
inline int Add(int x, int y) { x += y; if (x >= mod) x -= mod; return x; }
inline int Sub(int x, int y) { x -= y; if (x < 0) x += mod; return x; }

int n, m, k, fac[maxn], ivf[maxn], f[maxn], g[maxn], rev[maxn];

void dft(int *a, int lim) {
  int k = __builtin_ctz(lim);
  rep (i, 1, lim - 1) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (k - 1));
  rep (i, 0, lim - 1) if (i < rev[i]) swap(a[i], a[rev[i]]);
  for (int len = 1; len < lim; len <<= 1) {
    int rt = fpw(3, (mod - 1) / (len << 1));
    for (int l = 0; l < lim; l += (len << 1)) {
      int wn = 1;
      for (int i = 0; i < len; ++i, wn = 1ll * wn * rt % mod) {
        int x = a[l + i], y = 1ll * a[l + i + len] * wn % mod;
        a[l + i] = x + y, a[l + i + len] = x - y;
        if (a[l + i] >= mod) a[l + i] -= mod;
        if (a[l + i + len] < 0) a[l + i + len] += mod;
      }
    }
  }
}

void idft(int *a, int lim) {
  reverse(a + 1, a + lim), dft(a, lim);
  int k = fpw(lim, mod - 2);
  rep (i, 0, lim - 1) a[i] = 1ll * a[i] * k % mod;
}

int binom(int x, int y) {
  if (x < 0 || y < 0 || x < y) return 0;
  return 1ll * fac[x] * ivf[y] % mod * ivf[x - y] % mod;
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  cin >> n >> m >> k;
  fac[0] = 1;
  rep (i, 1, n * m) fac[i] = 1ll * fac[i - 1] * i % mod;
  ivf[n * m] = fpw(fac[n * m]);
  per (i, n * m, 1) ivf[i - 1] = 1ll * ivf[i] * i % mod;
  int ans = 0, lim = 1;
  while (lim <= 2 * n * m) lim <<= 1;
  rep (i, 0, n * m) if (k - i >= 0) f[i] = 1ll * ((i & 1) ? mod - 1 : 1) * ivf[i] % mod * ivf[k - i] % mod;
  rep (i, 0, n * m) if (n * m - i - k >= 0) g[i] = 1ll * ivf[i] * ivf[n * m - i - k] % mod;
  dft(f, lim), dft(g, lim);
  rep (i, 0, lim - 1) f[i] = 1ll * f[i] * g[i] % mod;
  idft(f, lim);
  rep (x, 0, n) rep (y, 0, m) {
    int cnt = x * (m - y) + y * (n - x);
    // rep (p, 0, cnt) {
    //   if (k - p >= 0 && n * m - cnt - (k - p) >= 0)
    //   add(sum, 1ll * ((p & 1) ? mod - 1 : 1) * ivf[cnt - p] % mod * ivf[p] % mod * ivf[k - p] % mod * ivf[n * m - (cnt - p) - k] % mod);
    // }
    add(ans, 1ll * f[cnt] * fac[cnt] % mod * fac[n * m - cnt] % mod * 
             binom(n, x) % mod * binom(m, y) % mod * (((x + y) & 1) ? mod - 1 : 1) % mod);
  }
  rep (i, 1, n + m) ans = 1ll * ans * iv2 % mod;
  cout << ans << '\n';
}