Inverting a sentence which includes 'never ever'

Never will I ever take up smoking.

The test asks (not a homework) if it is correct or incorrect; I circled 'incorrect' but according to the answer key, it is correctly inverted.

Wouldn't the original sentence be 'I will never ever take up smoking'? If so, I think the adverbial is 'never ever' and I thought the inversion should be 'Never ever will I take up smoking'. How does the correct answer is correct?

The test is on this website

Both your inversion "Never ever will I take up smoking" and the version in the test "Never will I ever take up smoking" are possible. They both have a negative adverb and an inverted verb-subject.

The second is more formal, the first is slightly childish. The function of the word "ever" is to intensify the adverb "never", but it is not part of the adverb.