Shuffled Stones

While walking down the street, Chanwoo found $2N$ stones on the ground, with the integers from $1$ to $2N$ written on them in order. Bothered by the neat order, he decided to shuffle the stones. He grouped the $2N$ stones into $N$ pairs of two, then swapped the positions of the two stones in each pair. This produced a new sequence $\{a_1,a_2,\ldots,a_{2N}\}$.

Pleased with the mess he had made, Chanwoo noticed an interesting property. The longest decreasing subsequence of the shuffled sequence has length only $2$. He wanted to take a photo of it, but his phone battery was dead. Instead, he took one pair of stones $(X,Y)$ that he had paired.

Back home, Chanwoo wanted to reconstruct the sequence, but he remembers only three things: $X$ and $Y$ were paired, the total number of stones is $2N$, and the longest decreasing subsequence of the sequence has length $2$. Given $2N$ and the pair $X$, $Y$, count how many sequences satisfy these conditions.

The first line contains $N$, $X$, and $Y$ separated by spaces. ($1 \le N \le 500\,000$; $1 \le X, Y \le 2N$; $X \ne Y$)

Print the number of valid sequences modulo $998\,244\,353$.

You can form a subsequence by removing some numbers from a sequence. Among the subsequences formed this way, the longest one sorted in decreasing order is called the longest decreasing subsequence.