Three targets $A$, $B$, and $C$ are placed in front of Mog. Each target is divided into $N$ regions of equal area, and a single number is written in each region. The numbers written in all regions are distinct, and there are no duplicate numbers across the three targets. That is, every number written on region is unique. Mog will shoot one arrow at each target. Because Mog is not good at handling a bow, the probability of an arrow hitting each region in a target is equal. There is no case where an arrow misses the target. Find the probabilities that the target with the largest number among the three numbers hit by the arrows is $A$, $B$, and $C$, respectively. When printing the probability $p$, you should print it as follows. If $p=\frac{x}{y}$, where $x$ and $y$ are integers and $y \not\equiv 0 \pmod{998\ 244\ 353}$, output the remainder of $x \cdot y^{-1}$ divided by $998\ 244\ 353$. It is guaranteed that $y \not\equiv 0 \pmod{998\ 244\ 353}$.

The input is given in the following format.

$N$ $A_1$ $A_2$ $\cdots$ $A_N$ $B_1$ $B_2$ $\cdots$ $B_N$ $C_1$ $C_2$ $\cdots$ $C_N$

Print the probabilities that the target with the largest number among the three numbers hit by the arrows is $A$, $B$, and $C$, respectively, modulo $998\ 244\ 353$.

• $1 \le N \le 300\,000$.
• $1 \le A_i, B_i, C_i \le 10^9$.
• $\{A_1, A_2, \cdots, A_N, B_1, B_2, \cdots, B_N, C_1, C_2, \cdots, C_N\}$ are distinct.