Unpredictable loop variables. Consider the following function: def func (lst: List[int]) -> None: n = len (1st) i = 0 3 4 j = 1 while i < n: if 1st [i] >= 0: i = i + j 6 7 8 else: 1st [i] = abs (1st [i]) 9 i = 0 10 j = j * 2 11 Find, with proof, an input family for func whose running time is O(log n). Find, with proof, an input family for func whose running time is O(n) and for which the else branch (Lines 9-11) executes N(logn) times. To simplify your analysis, you may assume n (the length of the list) is a power of 2." You may use the following formula, valid for all n N and r E R where r+ 1: n-1 1- rn 1-r i=0 Prove that the worst-case running time for func is O(n).