Geometry plus functions

Geometry Level 4

\[ \large\begin{cases} {A=(x,y) : x^2 + y^2 - 2|x| - 2|y| + 1= 0} \\ { B = (x,y) : y = mx + c } \end{cases} \]

If \(A \cap B \) is a non-empty set for all real numbers \(m\), what is the number of integral values of \(c\)?

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