Consider the following algorithm outline for finding the maximum, second$-$largest and third largest in a list of n keys. Initially: List contains n keys $($assume n is a power of $2)$ While List size n $2$ For every pair of keys Find the larger $($ store the loser in a loser list for the winner$)$ Let List contain the n$/2$ winners End. Now List contains Maximum $($Winner$).$ Second$\_$largest $=$ max$($ list of losers to Maximum$).$ Third$\_$largest $=$ max$(($list of losers to maximum $$ second$\_$largest$)$ U list of losers to second$\_$largest $)$ a$-$ Find the exact number of key comparisons made by the above algorithm. b$-$ Find the amount of extra space required by the algorithm? c$-$ Apply the algorithm to the following set of keys and show the Loser Lists. $10503090401007060$