Gomgom and the Tournament

Gomgom is going to enter the Gomgom Dance Tournament, where $2^K$ participants compete to pick the best Gomgom dancer.

The tournament has $K$ rounds. In each round, participants are paired off in twos and dance against each other.

In the $i$-th round ($1 \leq i \leq K$), the winner receives $r\_i$ won in prize money. If it is not the final round, the winner advances to the next round. A loser is eliminated and goes home.

Participant $i$ ($1 \leq i \leq 2^K$) has a dance skill score $a\_i$. When two participants meet, the one with the higher score always wins.

[Figure 1] One of the 24 possible brackets when there are 4 participants. The number in each circle is the participant number.

The bracket is chosen at random before the tournament starts, from the $(2^K)!$ possible arrangements. Every arrangement is equally likely.

Gomgom learned that the prize money he can win depends on how the bracket is made.

Given the dance skill scores of Gomgom and the other participants, compute the expected prize money Gomgom can take home.

The first line contains the number of rounds $K$. $(1 \leq K \leq 18)$

The second line contains the dance skill scores $a\_1, ..., a\_{2^K}$ of the participants, separated by spaces. $(1 \leq a\_i \leq 10^9)$

The third line contains the prize money $r\_1, ..., r\_K$ for each round, separated by spaces. $(1 \leq r\_i \leq 10^6)$

All dance skill scores are distinct, so no ties occur.

Gomgom is participant $1$.

All input values are positive integers.

It can be proven that the expected prize money Gomgom can earn in the tournament is always a rational number. Write the expected value as $\frac{y}{x}$ where $x$ and $y$ are coprime. There is exactly one integer $z$ with $0 \leq z \leq 998\ 244\ 352$ that satisfies $xz \equiv y \pmod {998\ 244\ 353}$.

Print $z$.