Let $\mathcal{A}$ be the set of first hundred natural numbers.

A function $f(t)$ is defined from $\mathcal{A}$ to $\mathbb{R}$ which denotes the sum of of infinite geometric series whose first term is $\frac{t-1}{t!}$ and the common ratio is $\frac{1}{t}$.

Let $S(n)$ denote the sum:

$S(n) = \sum_{r=1}^n | (r^2-3r+1)f(r) |$

Find the value of $\frac{100^2}{100!} + S(100)$.

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