Use input inside a spreadtab environment with calculations

Use input inside a spreadtab environment with calculations

My aim is to create a command for inserting tables, which will format the
table, and add calculations on its values, given a file containing the raw
data of the rows only.
\begin{spreadtab}{{tabular}{lcc}}
\toprule
@ Product name & @ Price & @ Count \\
\midrule
\input{products}
\midrule
@ Total & :={sumprod(b2:[0,-1];c2:[1,-1])} & sum(c2:[0,-1])\\
\bottomrule
\end{spreadtab}
where products.tex includes
@ Plant & 60 & 2 \\
@ Book & 90 & 4 \\
@ Other & 100 & 10 \\
Pasting the lines of products.tex into the matching place above works
smoothly.
I wish to have the above code as a command, so I can use the same code to
enter different table values, without repeating the heading and
calculation definitions. However, the end result of using input always
leaves the summation values as 0, and the @ letter is now part of the
text:

I guess the processing by spreadtab is done before the input is inserted -
but I wonder if there is a way to solve it.
Following this question: Cannot use \toprule when doing \input inside
tabular -- why?, I tried to add primitive tex input into the spreadtab
environment. Meaning, I used
\makeatletter
\newcommand\primitiveinput[1]{\@@input #1 }
\makeatother
and replaced the line \input{products} with \primitiveinput{products}. But
again no luck - I get the exact same output as using input.
Any ideas?