LibreOffice Calc formula to count the number of sheets named like `SomePrefix$i`, e.g. `Sheet1`, `Sheet2`, …

I’ve got a spreadsheet file with multiple sheets. The sheet names are composed of some prefix (e.g. Foo or Bar) and a number, which is counted from 1.

Let’s start from a file with 5 sheets named as follows:
Foo1, Foo2, Bar1, Bar2, Bar3

I’d like to have a function (not a macro) to count the number of sheets with a specific prefix.
In the example above, the result for Foo would be 2, for Bar it would be 3.