Ana and Banana are playing a game. Initially, Ana secretly picks a number 1≤A≤106. In each subsequent turn of the game, Banana may pick a positive integer B, and Ana will reveal to him the most common digit in the product A⋅B (written in decimal notation). In the case when at least two digits are tied for being the most common, Ana will reveal all of them to Banana. For example, if A⋅B=2022, Ana will tell Banana that the digit 2 is the most common, while if A⋅B=5783783, Ana will reveal that 3,7 and 8 are the most common. Banana's goal is to determine with certainty the number A after some number of turns. Does he have a winning strategy? number theoryDigitsguessing game