Number theory ultimatum by Rohith, Anirudh and Arjun!

\( a^{2} + b^{2} + c^{2} = 2(a+b+c+1) \) and
\( ab+bc+ca = a^{2} + b^{2} + c^{2} - c \)

Let \(a, b, c \) are positive integers which satisfy the equations above, find \( a + b + c \).

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