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java - make characters optional in regular expression

I am trying to validate a (US) phone number with no extra characters in it. so the format is 1-555-555-5555 with no dashes, spaces, etc and the 1 is optional. However, my regular expression will ONLY except numbers with the leading 1 and says numbers without it are invalid. Here is what I am using where did I go wrong?

"^(1)\d{10}$"
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Use:

"^1?\d{10}$"

The ? means "optional".


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