Narrower Passageway

You are a strategist of The ICPC Kingdom. You received intel that monsters will attack a narrow passageway near the kingdom. The passageway is a grid with $2$ rows (numbered from $1$ to $2$) and $N$ columns (numbered from $1$ to $N$). Denote $(r, c)$ as the cell in row $r$ and column $c$. Every day, a soldier with power $P_{r,c}$ is assigned to protect $(r, c)$.

The passageway is very foggy. Within a day, each column has a $50\%$ chance of being covered in fog. If a column is covered in fog, the two soldiers assigned to that column are not deployed that day. Otherwise, the assigned soldiers are deployed.

A connected area $[u, v]$ ($u \le v$) is a maximal set of consecutive columns from $u$ to $v$ (inclusive) such that no column in the set is covered in fog. The image below shows an example. The gray cells are covered in fog. There are $4$ connected areas: $[1, 2]$, $[4, 6]$, $[9, 9]$, and $[11, 11]$.

The strength of a connected area $[u, v]$ is computed as follows. Let $m_1$ and $m_2$ be the maximum power of the soldiers in the first and second rows of the connected area, respectively. Formally, $m_r = \max(P_{r,u}, P_{r,u+1}, \dots, P_{r,v})$ for $r \in \{1, 2\}$. If $m_1 = m_2$, then the strength is $0$. Otherwise, the strength is $\min(m_1, m_2)$.

The total strength of the deployment is the sum of the strengths of all connected areas. Determine the expected total strength of the deployment on any single day.

The first line contains an integer $N$ ($1 \le N \le 100\,000$).

Each of the next two lines contains $N$ integers $P_{r,c}$ ($1 \le P_{r,c} \le 200\,000$).

Let $M = 998\,244\,353$. It can be shown that the expected total strength can be expressed as an irreducible fraction $\frac{x}{y}$, where $x$ and $y$ are integers and $y \not\equiv 0 \pmod M$. Output an integer $k$ in a single line such that $0 \le k < M$ and $k \cdot y \equiv x \pmod M$.