Please solve the programming task below using a self-contained code snippet in a markdown code block.

Given a date string in the form Day Month Year, where:

Day is in the set {"1st", "2nd", "3rd", "4th", ..., "30th", "31st"}.
Month is in the set {"Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"}.
Year is in the range [1900, 2100].

Convert the date string to the format YYYY-MM-DD, where:

YYYY denotes the 4 digit year.
MM denotes the 2 digit month.
DD denotes the 2 digit day.

 
Please complete the following python code precisely:
```python
class Solution:
    def reformatDate(self, date: str) -> str:
```