Consider the following Syntax-Directed Translation (SDT) scheme with the grammar rules and actions provided below:
$$
\begin{aligned}
& S \rightarrow S_1 \# T\left\{S . \mathrm{val}=S_1 . \mathrm{val}-T . \mathrm{val}\right\} \\
& S \rightarrow T\{S . \mathrm{val}=T . \mathrm{val}\} \\
& T \rightarrow T_1 \% i d\left\{T . \mathrm{val}=T_1 . \mathrm{val} \times i d . \mathrm{val}\right\} \\
& T \rightarrow i d\{T . \mathrm{val}=i d . \mathrm{val}\}
\end{aligned}
$$
What is the value of $S.\mathrm{val}$ for the input expression$: 10 \# 2 \% 3 \# 4$?
