The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ______.

1
\(\pi[(b^2 -a^2) - \frac{n}{4}(b-a)^2]\)
2
\(\pi[(b^2 -a^2) - n(b-a)^2]\)
3
\(\pi[(b^2 -a^2) + \frac{n}{4}(b-a)^2]\)
4
\(\pi[(b^2 -a^2) + n(b-a)^2]\)

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