fun trace_string(m,str)=let
  val (bs,cs,rs)=(String.concat(m),String.size(List.hd(m)),List.length(m))
  val az=cs*rs
  fun at(f)=Array.tabulate(az,f)
  fun cib(c,r)=c>=0 andalso r>=0 andalso c<cs andalso r<rs
  fun cti(c,r)=r*cs+c
  fun itc(i)=(i mod cs,i div cs)
  val ncd=[(~1,~1),(0,~1),(1,~1),(~1,0),(1,0),(~1,1),(0,1),(1,1)]
  fun pno(c,r)=List.map(fn(cd,rd)=>(c+cd,r+rd))ncd 
  fun nf(c,r)=map cti(List.filter cib(pno(c,r))) 
  val nbs=at(fn(i)=>nf(itc(i)))
  fun son(a,nb)=List.foldl(fn(n,s)=>Array.sub(a,n)+s) 0 nb;
  fun cv(a,i,chr,f)=if String.sub(bs,i)=chr then f+son(a,Array.sub(nbs,i))else 0
  fun wp(a,[],_)=Array.foldl(op +)0 a|wp(a,c::cs,f)=wp(at(fn(i)=>(cv(a,i,c,f))),cs,0)     
in wp(Array.array(az,0),explode(str),1) end;