Bertha has $6$ daughters and no sons. Some of her daughters have $6$ daughters, and the rest have none. Bertha has a total of $30$ daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children? Fill in the blank with the correct number.

Let's think step by step and output the final answer within \boxed{}.
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