Create a PDA that recognizes the following context free language with terminals $\{$a$,$b$\}$

L $=\{$w $|$ number of a$$s $=$ twice the number of b$$s; String w can only have a$$s followed by b$$s or

b$$s followed by a$$s$\}$

i$.$e$.,$ it should accept aab, aaaabb, baa, bbaaaa,.. and so on$.$

$($i$)$ Describe your algorithm

$($ii$)$ Give the description as a complete $7-$tuple with a transition diagram

$($iii$)$ Show configuration sequences on aaaabb leading to acceptance.