Q55

Consider the following grammar along with translation rules.

$$\begin{aligned} & S \rightarrow S_{1} \# T \qquad \{S._{\text{val}} =S_{1}. _{\text{val}} \; ^{\ast} T._{\text{val}}\}\\ & S \rightarrow T \qquad \qquad \{S._{\text{val}} = T._{\text{val}}\}\\ & T \rightarrow T_{1} \% R \qquad \{T._{\text{val}} =T_{1}._{\text{val}} ÷ R._{\text{val}}\}\\ & T \rightarrow R \qquad \qquad \{T._{\text{val}} = R._{\text{val}}\} \\ & R \rightarrow \text{id} \qquad \qquad \{R._{\text{val}} = \text{id}._{\text{val}}\} \end{aligned}$$

Here $\#$ and $\%$ are operators and $\text{id}$ is a token that represents an integer and $\text{id}._{\text{val}}$ represents the corresponding integer value. The set of non-terminals is $\{\text{S, T, R, P}\}$ and a subscripted non-terminal indicates an instance of the non-terminal. Using this translation scheme, the computed value of $S._{\text{val}}$ for root of the parse tree for the expression $20 \# 10 \% 5 \# 8 \% 2 \% 2$ is ________________.