Doubly symmetric

What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?
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Problem



Image
Doubly Symmetric


What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order $2$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.