candies :$[2,3,5,2]$

if a$=2,$ b$=3,$ c$=5,$ and d$=2,$ The child can increase any of these integers by $1$ at most $4$ times. If the child picks integer c and integer d to increase each of them twice, the new values will become a$=4,$ b$=3,$ c$=5,$ and d$=4.$ Accordingly, the child will get $4$x$3$x$5$x$4=240$ candies. In any given case, what is the maximum value of a x b x c x d the child can achieve with these operations?

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a$)$ Design an algorithm to solve this problem with the least possible complexity,

b$)$ Analyses the complexity of your solution.

c$)$ Develop a python code to implement your efficient algorithm. $[$The marks depend on the correctness of the code, indentation, comments, test$-$case$]$