long N=1024,d[1<<16]={1},A[1025],r;k,n,m,x,y,i;main(a){for(;~scanf("%d",&a);)n?k+=A[a]?0:++A[a]:(n=m,m=x,x=y,y=a);for(;i<n*N;++i){for(m=N;m--;)d[i+N^m]+=A[m]*d[i];d[i+N*2]-=i?d[i]*k:k--;}for(;x<N&x<=y;)r+=d[i+x++];printf("%d",r%998244353);}