A woman came to a market to sell some eggs. A first buyer took half her eggs plus 1⁄2 an egg. The same happened with the remaining eggs: a second buyer took half her eggs plus 1⁄2 an egg. A third buyer took half of her remaining eggs plus 1⁄2 an egg. A fourth buyer took half of her remaining eggs plus 1⁄2 an egg. The woman then sold her last remaining egg to the fifth buyer. How many eggs were there initially if the woman never broke an egg? Show your steps.