#include<bits/stdc++.h>
using namespace std;
const int mod=998244353,mx=5e5;
int fac[500005],ifac[500005];
int mul(int a,int b){return 1ll*a*b%mod;}
void add(int &x,const int y){if((x+=y)>=mod)x-=mod;}
void sub(int &x,const int y){if((x+=(mod-y))>=mod)x-=mod;}
int C(int n,int m){if(n<m)return 0;return mul(fac[n],mul(ifac[m],ifac[n-m]));}
int n,m,k,Wn[1<<21|1],f[1<<21|1],g[1<<21|1],limit,L,r[1<<21|1];
int qpow(int a,int b){
	int c=1;
	while(b){if(b&1)c=mul(c,a);a=mul(a,a),b>>=1;}
	return c;
}
void ntt(int *a,int o){
	for(int i=0;i<limit;++i)if(i<r[i])swap(a[i],a[r[i]]);int now=3;if(o<0)now=qpow(3,mod-2);
	for(int m=1;m<limit;m<<=1){
        int Gi=qpow(now,mod/(m<<1));
        Wn[0]=1;for(int j=1;j<=m;++j)Wn[j]=mul(Wn[j-1],Gi);
        for(int i=0;i<limit;i+=(m<<1))
         for(int j=0;j<m;++j){
         	int x=a[i+j],y=mul(a[i+j+m],Wn[j]);
         	a[i+j]=x+y,a[i+j+m]=x+mod-y;
         	if(a[i+j]>=mod)a[i+j]-=mod;
         	if(a[i+j+m]>=mod)a[i+j+m]-=mod;
		 }
	}
	if(o<0){
		int inv=qpow(limit,mod-2);
		for(int i=0;i<limit;++i)a[i]=mul(a[i],inv);
	}
}
int main(){
	cin>>n>>m>>k;
	fac[0]=ifac[0]=ifac[1]=1;
	for(int i=1;i<=mx;++i)fac[i]=mul(fac[i-1],i);
	for(int i=2;i<=mx;++i)ifac[i]=mul(ifac[mod%i],mod-mod/i);
	for(int i=1;i<=mx;++i)ifac[i]=mul(ifac[i],ifac[i-1]);
    limit=1,L=0;while(limit<=2*n*m)limit<<=1,++L;
    for(int i=0;i<limit;++i)r[i]=((r[i>>1]>>1)|((i&1)<<L-1));
    for(int i=0;i<=k;++i){
    	f[i]=mul(ifac[i],ifac[k-i]);
    	if(i&1)f[i]=(mod-f[i])%mod;
	}
	for(int d=0;d<=n*m;++d)if(n*m-k-d>=0)g[d]=mul(ifac[n*m-k-d],ifac[d]);
	ntt(f,1),ntt(g,1);
	for(int i=0;i<limit;++i)f[i]=mul(f[i],g[i]);ntt(f,-1);
	for(int i=0;i<=n*m;++i)f[i]=mul(f[i],mul(fac[i],fac[n*m-i]));
	int ans=0;
	for(int i=0;i<=n;++i)
	  for(int j=0;j<=m;++j){
	  	int ct=(n-i)*j+i*(m-j);
	  	if((i+j)&1)sub(ans,mul(f[ct],mul(C(n,i),C(m,j))));
	  	else add(ans,mul(f[ct],mul(C(n,i),C(m,j))));
	  }
	int inv2=(mod+1)/2;
	for(int i=1;i<=n+m;++i)ans=mul(ans,inv2);
	cout<<ans;
	return 0;
}