Fill in the Action and Goto tables for an LALR parser for the grammar given below, where the start symbol is E. “∧” is the power operator, i.e., x ∧ y means x^{y}. Although the grammar is ambiguous, your parser must not be ambiguous: an ambiguous string must be parsed according to the precedence of operators defined for Python. The power operator is right-associative and binds more tightly than unary operators on its left and less tightly than unary operators on its right. Thus a ∧ a ∧ a means a ∧ (a ∧ a), −a ∧ a means −(a ∧ a), and a ∧ −a means a ∧ (−a). Note: a represents any variable name.

1. E ⟶ E + E

2. E ⟶ E − E

3. E ⟶ E ∗ E

4. E ⟶ − E

5. E ⟶ E ∧ E

6. E ⟶ ( E )

7. E ⟶ id