Recursion: Exact Factorial Bounds

Create a recursive function that tests if a number is the exact upper bound of the factorial of n. If so, return a list that contains the exact factorial bound and n, or otherwise, the string "Not exact!".

Examples

is_exact(6) ➞ [6, 3]

is_exact(24) ➞ [24, 4]

is_exact(125) ➞ "Not exact!"

is_exact(720) ➞ [720, 6]

is_exact(1024) ➞ "Not exact!"

is_exact(40320) ➞ [40320, 8]

Notes

• It is expected from the challenge-takers to come up with a solution using the concept of recursion or the so-called recursive approach.
• There will be no exceptions to handle. All inputs are positive integers.
• A non-recursive version of this challenge (of lesser difficulty and which gives you the total liberty of not using the recursive approach) can be found in here.