Juku has the first $100$ volumes of the Harrie Totter book series at his home. For every $i$ and $j$, where $1 \le i < j \le 100$, call the pair $(i, j)$ reversed if volume No. $j$ is before volume No. $i$ on Juku’s shelf. Juku wants to arrange all volumes of the series in one row on his shelf in such a way that there do not exist numbers $i, j, k$, where $1 \le i < j < k \le 100$, such that pairs $(i, j)$ and $(j, k)$ are both reversed. Find the largest number of reversed pairs that can occur under this condition.

Let's think step by step and output the final answer within \boxed{}.
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