Number of digits of a factorial

Number Theory Level pending

The factorial of 23 = 25 852 016 738 884 976 640 000, and as you can see, have 23 digits (including the zeros at the end) as the number itself. Another 2 numbers where the number of digits of its factorial are equal to the number itself are: 22 and 24. What is the odd number where the number of digits of its factorial is exactly ten times the number?

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