Now its very strenuous

Algebra Level 4

Three positive real numbers $$a$$, $$b$$, and $$c$$ satisfy the following equation. $\large a+b+c=abc$ Let $\large N = 3+\dfrac{b}{a^2}+\dfrac{c}{b^2}+\dfrac{a}{c^2}-\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)^2$ If the minimum value of $$N$$ can be expressed as $$\sqrt{x}$$, where $$x$$ is square free positive integer. Find $$x$$.

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