Flexible Range Formula

I need a formula that will return the minimum value from a column range that flexs without having to manually go in an change row references. There is a blank row between each section of data in order to separate info.

As an example:
Assumes Column A
Row 5 = 11
Row 6 = 12
Row 7 = 9
Blank Row
Row 9 = 12
Row 10 = 11
Row 11 = 15
Row 12 = 6
Row 13 = 11
Blank Row

Need to formula to flex to include rows 5 thru 7 in the first section but expand to include rows 9 thru 13 in the second section. =MIN(A5.A7) works but how do I get next section to flex to =MIN(A9.A13) without manually changing the cell references? There is always a blank row in between the sections to separate.

Any help that you can send my way would be greatly appreciated.

It would help if you outline where these MIN formulae are to be located in reference to the source values.

Sorry about that ... should have given more info.
Column A contains the values (month number).
Column B contains the formula =MIN.
The number of rows in column A flex and are separated by a blank row.
Data is separated by this blank row into individual sections.
The =MIN formula is always on the first row of each individual section in Column B.
Want to be able to copy the formula down column B without having to manually adjust the number of rows in the =MIN formula. Need a formula that would be able to tell the number of rows in each section in Column A and then return the minimum value for that section in Column B.

Month MIN
11 9
12
9

12 6
11
15
6
11

9 7
12
7
7

Hope that this is a little clearer. Thanks in advance for your suggestions.

I don't how many data points you have in total, but in terms of general principle...one approach might be:

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