Provide an example of a context$-$free grammar over the alphabet $\{$a$,$ b$,$ c$\}$ that is LL$(1)$ but is not LALR$(1).$ In your answer:

a$.$ Present the grammar.

b$.$ Compute the First and Follow functions for each of the grammar's variables.

c$.$ Construct the parsing table for a predictive parser for the grammar. Show that there are no conflicts in this parsing table.

d$.$ Build the LR$(1)$ items automaton for the extended grammar.

e$.$ Construct the parsing table for a canonical LR$(1)$ parser $($including the Action and Goto parts$).$ Show that there are no conflicts in this parsing table.

f$.$ Explain in detail why the grammar is not LALR$(1).$