The Small Castle Built by a Dwarf

$N$ castles stand in a row. The current height of castle $i$ is a positive integer $H_i$.

The dwarf may change every height to any positive integer. Increasing the height of castle $i$ by one costs $A_i$, and decreasing it by one costs $B_i$.

Let the resulting heights be $H'_i$. The castles are harmonious if

for every $1 \leq i < N$. Find the minimum cost required to make the castles harmonious.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$N$ $H_1\ H_2\ \cdots\ H_N$ $A_1\ A_2\ \cdots\ A_N$ $B_1\ B_2\ \cdots\ B_N$

For each test case, print the minimum cost modulo $998\,244\,353$.

• $1 \leq T \leq 100$
• $1 \leq N \leq 200\,000$
• $1 \leq H_i,A_i,B_i \leq 10^9$ ($1 \leq i \leq N$)
• The sum of $N$ over all test cases does not exceed $200\,000$.