ll@(++N,M,K),@(X,Y)[N],@(A,B)[K],L=1d3,x;auto D=[&](ll&x,ll&y,ll i){return(x-X[i])**2+(y-Y[i])**2;};VLL o(K,1e18);VVI l(N);Timer t;t.set();Rand r;while(t.get()<5){x=r.get(L);rep(j,N)l[j]={X[j]*x+Y[j],j};sortV(l);rep(i,K){VI s{A[i]*x+B[i],0};M=bsearch_min[ll,m,0,N](s<l[m]);rep(j,max(0,M-L),min(N,M+L))o[i]<?=D(A[i],B[i],l[j][1]);}}M=min[j,1,N](D(*X,*Y,j));rep(i,K)A[i]=D(A[i],B[i],0);Wt(sum[i,0,K](min(sqrt(A[i]),sqrt(M)+sqrt(o[i]))*2));