Your daughter's high school Introduction to Engineering class includes a week$-$long exposure to an oil refractory. The model facility built by the teacher involves $6$ steps, and it's obvious that most of the steps have significant leakage. If the teacher wants to have $164$ ounces of product when the process is complete, how many ounces of ingredients must they begin with? The process has the following scrap rates for the corresponding step:

Step $1$: $1\mathrm{.}8\%$

Step $2$: $0\mathrm{.}9\%$

Step $3$: $1\mathrm{.}1\%$

Step $4$: $2\mathrm{.}4\%$

Step $5$: $0\mathrm{.}6\%$

Step $6$: $0\mathrm{.}1\%$

$($Keep one decimal point in your answer$)$