Product Digits

Have the function ProductDigits(num) take the num parameter being passed which will be a positive integer, and determine the least amount of digits you need to multiply to produce it. For example: if num is 24 then you can multiply 8 by 3 which produces 24, so your program should return 2 because there is a total of only 2 digits that are needed. Another example: if num is 90, you can multiply 10 * 9, so in this case your program should output 3 because you cannot reach 90 without using a total of 3 digits in your multiplication.

Examples

Input: 6
Output: 2

Input: 23
Output: 3