Hi. I'm moving the sink in my kitchen to the other side of the room. There is a bathroom about 10 feet away with it's own dedicated drain and vent stack. Can I vent my new sink by going up to the ceiling, about a 6 foot rise, over to the existing sink, about 10 feet down to the existing vent, about 4 feet, and tie into it there. From there on it vents to the main stack. It will be tying into the vent above the top of the proposed sink. Thanks in advance.