I think rectangular forest deserves a proper PDL solution. Answer is 1698, same as running GrandFather's code.

use strict;
use warnings;
use PDL;

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;
{
    my @s = map $t4-> slice( "X, X, $_" ), 0 .. 3;
    $s[ 1 ] .= $s[ 1 ]-> copy-> transpose;
    $s[ 2 ] .= $s[ 2 ]-> copy-> slice( '-1:0, X' );
    $s[ 3 ] .= $s[ 3 ]-> copy-> transpose-> slice( '-1:0, X' );
}
my $cummax = maxover $SLTM * $t4-> dummy( 1 );
my $seen   = $t4 > $cummax;
{
    my @s = map $seen-> slice( "X, X, $_" ), 0 .. 3;
    $s[ 1 ] .= $s[ 1 ]-> copy-> transpose;
    $s[ 2 ] .= $s[ 2 ]-> copy-> slice( '-1:0, X' );
    $s[ 3 ] .= $s[ 3 ]-> copy-> slice( '-1:0, X' )-> transpose;
}
print $seen-> mv( -1, 0 )-> orover-> sum;

__END__
0021000302223413032321152215243115022004032344522041252513450244235444
+43305142410110142101223120110
... skipped, see 11148843
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