$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$_____________________$__________________________$$$$$$$$$$$$
$$$$$$$$$$$$____________________$$$_________________________$$$$$$$$$$$$
$$$$$$$$$$$$__$_________________$$$________________$________$$$$$$$$$$$$
$$$$$$$$$$$$___$$______________$$$$$_____________$$_________$$$$$$$$$$$$
$$$$$$$$$$$$____$$$____________$$$$$___________$$$__________$$$$$$$$$$$$
$$$$$$$$$$$$_____$$$$$_________$$$$$________$$$$$___________$$$$$$$$$$$$
$$$$$$$$$$$$______$$$$$$$______$$$$$_____$$$$$$$____________$$$$$$$$$$$$
$$$$$$$$$$$$________$$$$$$$____$$$$$___$$$$$$$______________$$$$$$$$$$$$
$$$$$$$$$$$$___________$$$$$____$$$___$$$$$_________________$$$$$$$$$$$$
$$$$$$$$$$$$__$$$$$$$______$$$__$$$__$$$______$$$$$$$_______$$$$$$$$$$$$
$$$$$$$$$$$$______$$$$$$$$____$$_$_$$____$$$$$$$$___________$$$$$$$$$$$$
$$$$$$$$$$$$__________$$$$$$$$$_$$$_$$$$$$$$$_______________$$$$$$$$$$$$
$$$$$$$$$$$$_________________$$$_$_$$$______________________$$$$$$$$$$$$
$$$$$$$$$$$$_____________$$$$$___$___$$$$$__________________$$$$$$$$$$$$
$$$$$$$$$$$$_____________________$__________________________$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$