Docs for contour levels argument is incorrect #12729

Bug report

Bug summary

In 2.2.3 a sentence made it into the contourf docs saying for the levels of
contourf(x,y,z,levels, ....)

levels : int or array-like, optional
Determines the number and positions of the contour lines / regions.
If an int n, use n data intervals; i.e. draw n+1 contour lines. The level heights are automatically chosen.

The bold sentence is obviously wrong, as seen from the below image. E.g. the top right plot has n=4 specified, but it produces 5 intervals and 4 contour lines. When specifying n=5, the same 5 intervals and 4 contour lines are produced.

One may look at the generated levels as a function of the input argument,

This is because a MaxNLocator is used.

self.locator = ticker.MaxNLocator(N + 1, min_n_ticks=1)

The MaxNLocator docs say

Select no more than N intervals at nice locations.

I would deduce, that the contourf docstring should rather say

If an int n, use m data intervals, where m <= n+1; i.e. draw m-1 contour lines.

However, using different data, one may even find

locator = mticker.MaxNLocator(4+1, min_n_ticks=1)
print(len(locator.tick_values(-0.11109, 1-0.1111)))
# prints 7

locator = mticker.MaxNLocator(9+1, min_n_ticks=1)
print(len(locator.tick_values(-0.11109, 1-0.1111)))
# prints 12

which might suggest that also the MaxNLocator docstring is wrong, and should really say

Select no more than N+1 intervals at nice locations.

But maybe other data would even produce N+x intervals?

ToDo:

1. Find out how many intervals MaxNLocator is capable of producing.
2. Correct MaxNLocator docstring
3. Based on that, correct contourf docstring.