The product designer of the DooDad from the last question is dissatisfied with the reliability of the product when it consists solely of one component A and one component B in series. She wants to improve the reliability of DooDads by changing their structure. The new and improved DooDad will have a number of component A$\text{'}$s connected in parallel and one component B in series with the paralleled component A$\text{'}$s$,$ as depicted in the image below. As before, the reliability of component A is $0\mathrm{.}5$ and the reliability of component B is $0\mathrm{.}9.$

What is the fewest number of A$\text{'}$s that she needs to connect in parallel in order to get the reliability of the system to be greater than $0\mathrm{.}85?$