GATE CSE 2022 Q65: Evaluating an expression with a syntax-directed translation

Consider the following grammar along with translation rules.

$$\begin{aligned} S &\to S_1 \# T && \{S.val = S_1.val * T.val\} \\ S &\to T && \{S.val = T.val\} \\ T &\to T_1 \% R && \{T.val = T_1.val \div R.val\} \\ T &\to R && \{T.val = R.val\} \\ R &\to id && \{R.val = id.val\} \end{aligned}$$

Here $\#$ and $\%$ are operators and $id$ is a token that represents an integer and $id.val$ represents the corresponding integer value. The set of non-terminals is $\{S, T, R, P\}$ and a subscripted non-terminal indicates an instance of the non-terminal.

Using this translation scheme, the computed value of $S.val$ for root of the parse tree for the expression $20 \# 10 \% 5 \# 8 \% 2 \% 2$ is _____________.