Consider the following program which modifies an input array A:

def cool$($A$)$:

a $=1$

b $=1$

c $=1$

for i in range$($len$($A$))$:

if $2*($a$**3)==$ b$**3+$c$**3$: return

A$[$i$]=($a$,$ b$,$ c$)$

a $+=1$

b $+=1$

c $+=1$

Calculate, in terms of $\backslash$Theta complexity class, the worst$-$case complexity of the program above as a function of the size n of the input array A$.$ Justify your answer by giving a detailed calculation.

Hint: This question is relatively hard. You may, or may not, want to use the fact that, for any positive integers a$,$ b$,$ c$,$ we cannot have a$3=$ b$3+$ c$3.$

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