use strict;
use warnings;
use PDL;

sub turn_tables {
    my ( $pdl, $dir ) = @_;     # dir = 0   => cw
                                #       1   => ccw

    my @s = ( undef, map $pdl-> slice( "X, X, $_" ), 1 .. 3 );
    my @a = $dir ? ( 1, 2, 3 ) : ( 3, 2, 1 );
    
    $s[ $a[0]] .= $s[ $a[0]]-> copy
                            -> transpose-> slice( '-1:0, X' );  # 90
    $s[ $a[1]] .= $s[ $a[1]]-> copy
                            -> slice( '-1:0, -1:0' );           # 180
    $s[ $a[2]] .= $s[ $a[2]]-> copy
                            -> slice( '-1:0, X' )-> transpose;  # 270
}

my $trees = 1 + rcols *DATA, 
    { COLSEP => qr//, KEEP => qr/^\d+$/ }, [];
my $size = max shape $trees;
$trees-> reshape(( $size ) x 2 );

my $SLTM = identity( $size )
    -> cumusumover
    -> xor( identity $size )
    -> transpose;
    
my $t4 = $trees-> dummy( -1, 4 )-> copy;
turn_tables( $t4 );
my $cummax = maxover $SLTM * $t4-> dummy( 1 );
my $seen   = $t4 > $cummax;
turn_tables( $seen, 1 );

print $seen-> mv( -1, 0 )-> orover-> sum;

__END__
002100030222341303232115221524311502200403234452204125251345024423544443305142410110142101223120110
... skipped, see 11148843