\[\large \sum_{k=1}^{1800} \psi(k)\]

If the above sum can be expressed as \(aH_b-c\gamma-d\) for some not necessarily distinct positive integers \(a,b,c\) and \( d\), evaluate \(a+b+c+d\) where \(b,c\) is maximum possible.

**Notations**:

\(\psi(\cdot)\) represents the digamma function.

\(H_n\) denotes the \(n^\text{th}\) harmonic number.

\(\gamma\) represents the Euler-Mascheroni constant which is approxiamately equal to 0.5772.

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