Number Puzzle #19- The Five Thieves -

Five thieves were in a tavern and overheard a drunken shopkeeper bragging about his large collection of diamonds. Later that night, one of the thieves broke into the shop. He had a bit of a conscience (as far as thieves go) and only took half of the diamonds. But on his way out, he decided to take one more. After all, he was a thief. A while later, the second thief arrived. It was a night of odd coincidences. He also took half of the remaining diamonds plus one more. Shortly after, the third thief arrived and likewise took half of the remaining diamonds plus one more. Next, the fourth thief arrived and he as well took half of the remaining diamonds plus one more. Finally, the fifth thief arrived only to find that there were no diamonds left. How many diamonds did the shopkeeper have at the start?