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Default COUNTIF in between rows

How would I find the maximum amount of intervals between
"Larry" re- appearing in column A?
I must use a formula- not a macro or a filter.

The correct answer in this example= 4.
That means that in column A, the maximum absence (or intervals)
of "Larry" re- appearing was 4 times, which occured between rows
2 and 7. (Ex: As opposed to rows: 7 - 9, where he was only absent once)


Rows Column A

1 John
2 Larry
3 John
4 John
5 John
6 Mary
7 Larry
8 Mary
9 Larry
10 John
 
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