Two Rats, a male and a female arrive on a deserted island on January 1st. On that day the female rat gives birth to 8 babies, 4 male and 4 female. This same female rat will have a new group of babies every 40 days afterwards and each time she will have 8 babies, 4 male and 4 female. Every female rat born on this island will have her first group of babies 120 days after the female was born and then have a new group of babies every 40 days after that. Each time she will have 8 babies, 4 female and 4 male. If no rats die or leave the island, and they have plenty of food then determine how many total rats will be on this island on January 1st exactly 2 years after the original two rats arrived.