\[\dfrac{1}{a^4}+\dfrac{1}{b^4}+\dfrac{1}{c^4}=1\]

Given the above equation for positive numbers \(a,b,c\).

Find the minimum value of

\[\dfrac{a^4b^4+a^4c^4+b^4c^4}{a^3b^2c^3}\]

If the minimum value of the above is \(x\), input your answer as \(\lfloor 100x \rfloor\).

This is part of the set Trevor's Ten

**Details and Assumptions**

The answer is not \(300\).

It is indeed \(a^3 b^2 c^3\) and not \(a^3 b^3 c^3 \)

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