Question
Read a shared length and two integer vectors of that length, then return their dot product as a decimal string. Most entries are zero, so the useful work should follow the non-zero positions rather than the declared length.
```python
def solve(raw: str) -> str:
...
def run_case(case: dict) -> str:
return solve(case["stdin"])
```
## Requirements
- Line 1 is the length `n`; line 2 holds `n` integers for the first vector; line 3 holds `n` integers for the second.
- Some inputs carry the two characters backslash and `n` instead of real line breaks; treat both forms as line separators before parsing.
- Multiply matching positions, then add the products. Entries may be negative, so the sum can be negative or zero.
- Return the total as a plain decimal string with no padding, no plus sign, and no newline.
- Do not print the individual products or the operand vectors.
- Both vectors are read in full even when an entry is zero.
- Do not append a trailing newline to the returned string; return the value exactly once.