AI slop

You are given a sequence $a$ of length $2n$. Each integer from $1$ to $n$ occurs exactly twice.

Choose the deletion order of the elements uniformly from all $(2n)!$ orders. Delete the original elements one at a time in this order, preserving the relative order of the remaining elements.

For each integer $i$, earn $w_i$ points if its two occurrences are adjacent at least once, either initially or during the deletion process. Points for each integer are earned at most once. Let $S$ be the final score. Find the expected value of $S^2$.

If this expectation is the reduced fraction $p/q$, output $p\cdot q^{-1}$ modulo $998244353$, where $q^{-1}$ denotes the multiplicative inverse of modulo .

The input is given in the following format:

$n$ $a_1\ a_2\ \cdots\ a_{2n}$

Print the expected value of $S^2$ modulo $998244353$.

• $1\le n\le 200\,000$
• $1\le a_j\le n$ ().