One Pair for Each Creature

Newt wants to tidy up his magical creatures and split them into pairs. He has $n$ male creatures and $n$ female creatures. Every male creature stands on the x-axis, and every female creature stands on the y-axis. No creature is at the origin. Male creature $i$ is at $(x_i, 0)$, and female creature $i$ is at $(0, y_i)$. He wants to split all creatures into $n$ pairs, where each pair has one male and one female. For each pair, draw a segment between its two creatures. No two segments may intersect. Count the valid ways to form the pairs, and output the answer modulo $998\,244\,353$.

The first line contains one integer $n$ ($1 \le n \le 100\,000$). The second line contains $n$ integers $x_1, \ldots, x_n$ in increasing order ($-10^9 \le x_1 < \cdots < x_n \le 10^9$, $x_i \neq 0$). The third line contains $n$ integers $y_1, \ldots, y_n$ in increasing order ($-10^9 \le y_1 < \cdots < y_n \le 10^9$, $y_i \neq 0$).

Print one integer, the number of valid ways to form the pairs modulo $998\,244\,353$.