Nice photos! I wonder if it's not a hooded crow or something else because it looks grey in the area where magpies have a beautiful, clean white color. Also, the beak seems more humped than magpies have. There are some interesting photos of hooded crows on Wikipedia. The one photographed in Egypt is almost white in the "grey" area so it's pretty similar to a magpie. But I'm still not sure. What do you think? :)
https://en.wikipedia.org/wiki/Hooded_crow