#!perl -l
$_*=$z,($z)=/(.{0,6}?)0*$/for($z=1)..pop;print$z%10
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Just some last-minute tiebreaker silliness.
#!perl -l
$_*=$~,($~)=/(.{0,9}?)0*$/for($~=1)..pop;print$~%10
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#!perl -l
($z)=($z*$_)=~/(.{0,6}?)0*$/for($z=1)..pop;print$z%10
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Somehow I don't think this is ever going to get down to a reasonable length, but at least it works.
#!perl -l
sub'_{my($m,$n)=@_;$m=~s/.//||return;my$o=$&;my($p,$q)=split$o,$n;_(substr($m,0,length$p),$p)._(substr($m,length$p),$q).$o}print+_@ARGV
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