Three raids on the flock

Raiders took $\tfrac13$ of a flock of sheep plus $\tfrac13$ of a sheep. A second party took $\tfrac14$ of what remained plus $\tfrac14$ of a sheep. A third took $\tfrac15$ of the new remainder plus $\tfrac35$ of a sheep, leaving $409$ sheep. How many sheep were there originally? (No sheep were actually cut.)