Thanks. I just now managed to cut it down by quite a bit, but I think it looks too 'fat':

#!/usr/bin/perl
use strict;
use warnings;
;$"   =q%ef%;$_=q~my(   $i,$x,$y,$p)=(0   ,0,
0,p   op|         |5)   ;my         $r=   2<<
$p;my@i=m   ap[(1)x$r   ,2],1..$r   ;subi{$i[
            $x]               [$y
]--}i;sub   p{((1<$_[   0]?$y:$x)   -=1-($_[0
]&1   )*2         ,i)   for         -1,   1}s
ubf   {my($p,$f)=@_;$   p--;my@m=($f,3-   $f,
1-$                                       f);
my@o=(3-$   f,$f,$f,$f-2)if$p>0;(   $_&=3)for
      @o,   @m;               @o&   &f(
$p,pop@o)   ,@m&&p(po   p@m)while   (@o||@m)}
f$p               ,($   p&1               )*2
;su   bb{y,y491   02,   b#\   n,;print}   map
{bf   or@   $_}   @i~   ;y~    \n   ~~d   ;$;
.=1;s&b&b   &g;eval;#   %$_+28;($   x-={}for@
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I think that is too obscure