sub up{
		# indent to evidentiate the recursive function level
		# using the last index of the arguments array
		my $ind = ' ' x $#_ x 4;
		print $ind."\@_ = [@_]\n";
		my ($row, $col) = split /-/, $_[0];
		# if the first argument is 0-0 we are arrived to 
		# the upper edge: time to return the result
		if ($_[0] eq '0-0'){
			print $ind."RETURNING: \@_ is a valid path [@_]\n";
			return   "@_\n"
		}
		else{
			# check A 
			if ($row * $col > 0){
				# show what happens if check A pass
				print $ind."$row * $col > 0 ".
						"&& up(",$row-1,'-',$col-1,", ",(join ', ',@_),
						') # decremented both row and column are passed plus original @_ ',"\n";
			}
			else{
				print $ind."$row * $col > 0 is FALSE...\n";	
			}
			# execute the code if check A pass as shown above
			($row * $col > 0 && up( ~-$row . '-' . ~-$col, @_ ) ) .
			(	
				# check B
				eval{
					# show what happens if check B pass
					if ($row > $col){
						print $ind."$row > $col ".
							"&& up(",$row-1,'-',$col,", ",(join ', ',@_),
							') # decremented row and original column are passed plus original @_ ',"\n";
					}
					else{print $ind."$row > $col is FALSE...\n"}
					# the eval block return empty string
					# to not pollute the output of the function
					'';
				}				 
			).
			# execute the code if check B pass as shown above
			($row > $col && up( ~-$row . '-' . $col, @_ ) );
		} 
}