At the big glue stick party, Rob gives Sydney and Koreb as many glue sticks as each already has. Then Sydney gives Rob and Koreb as many glue sticks as each of them then has. Finally, Koreb gives Sydney and Rob as many glue sticks as each has. If, at the end of this avalanch of generosity, each person has sixteen glue sticks, how many glue sticks did each one have at the beginning?