CF1143B Nirvana

Kurt reaches nirvana when he finds the product of all the digits of some positive integer. Greater value of the product makes the nirvana deeper. Help Kurt find the maximum possible product of digits among all integers from $ 1 $ to $ n $ .

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In the first example the maximum product is achieved for $ 389 $ (the product of digits is $ 3\cdot8\cdot9=216 $ ). In the second example the maximum product is achieved for $ 7 $ (the product of digits is $ 7 $ ). In the third example the maximum product is achieved for $ 999999999 $ (the product of digits is $ 9^9=387420489 $ ).