The gardener sells half of his oranges plus three more to his first buyer. The gardener then sells half of his remaining oranges plus three more to his second buyer. Finally, the gardener sells half of his remaining oranges plus three more to his third buyer. The gardener is left with 13 oranges at the end of the day after the third (and final) buyer makes his purchase. Based on this information, how many oranges did the gardener start out with at the beginning of the day?