Don't break the eggs!

Level pending

My three children Aya, Nourhan and Omar were hungry and I had a basket of eggs. First I said to Aya, "Come and have half the number of the eggs in the basket plus half an egg provided that you break no egg." Aya did it without breaking any egg. I told Nourhan and Omar to do the same thing respectively. They were able to do it too. Checking the basket, I found it empty. How many eggs did I have at the very beginning?

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