Question 8: Consider the following recursive algorithm, which takes as input a sequence (ai, a2, . . . , an) of n numbers, where n is a power of two, i.e., n = 2k for some integer k-0: Algorithm MYSTERY(a,a.. ifn = 1 then return a1 else for i 1 to n/2 do bi = min(a2i-1, a2.) endfor; MYSTERY(bi, b2, ..., bn/2) endif Determine the output of algorithm MYSTERY(a1,a2,...,an). As always, justify your answer For any integer n 21 that is a power of two, let T(n) be the number of times that line (*) is executed when running algorithm MYSTERY(a1, a2,. . , an). Derive a recurrence for T(n) and use it to prove that for any integer n21 that is a power of two T(n) = n-1