First some terminology: A palindrome is any string the reads the same backwards or forwards. An example in English is the word "racecar". In the context of bitstrings $($sequences of $1\text{'}$s and $0\text{'}$s$)$ a palindrome would look list this $110001101100011.$ Again, in the context of bitstrings, an even$-$length bitstring palindrome is a string of the form w wr where w is any bitstring, and the superscript r means the reverse of w$.$ For example if w $=110001$ then wwr would be $110001100011.$

Now consider the language L of bitstrings that start with n $0\text{'}$s followed by an even length palindrome, followed by n$+11\text{'}$s$.$ In the preceding description, n can be any nonnegative integer. For example, the string $0001100111111$ would be in L since it is $03$ concatenated with $110011$ concatenated with $14$ and $110011$ is of the form wwr where w $=110.$

a$)$ Give a context free grammar for L

b$)$ Show how the string $0100111$ is generated by your grammar.

c$)$ Is your grammar ambiguous? Please explain why or why not.