# Magic trick

Leo, the magician asks a member of the audience to write down at most seven distinct prime numbers ($$>2$$) without showing them to Leo. Then the chosen member multiply each number with itself, and tells the amount of the perfect squares to Leo. From that in a few secundum (without using calculator) Leo finds out how many numbers did the member write down.

For example if Sarah was the chosen member, and she writes down the numbers $$3, 13, 23, 29,$$ then she tells the number $$3^2+13^2+23^2+29^2=1548$$.

Imagine that now you are the magician and you do the same trick (as Leo did) to your friend, Bob. Bob tells you the number $550632557$

How many numbers did Bob write down?

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