What's with that weird fraction?

Algebra Level 3

Let \(a_1,a_2,a_3,a_4\) be positive real numbers such that

\[a_1+a_2+a_3+a_4=52.\]

Let the maximum possible value of \(a_1a_2a_3a_4\) be \(P\).

Given that \(P\equiv n\pmod7\), find the value of \(\frac{n^3+n^2-n+1}{2}-1\).

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