E ach part (a and b) in this question is independent! a) Consider a binomial min-heap with n nodes! We know that the maximum key is at the root of a binomial tree. What is the nature of the number n (by nature of a number we mean for example: is it a prime number, a power of 3 , equal to 45 , divisible by 7 , etc )? D efine n 's most general, most comprehensive nature to cover all such binomial heaps. b) Consider a binomial max-heap BH with k=2n+2m14 nodes where m>n. 1. Which binomial trees is BH composed of? 2. The minimum key in BH is in the most crowded depth level of its largest binomial tree. What is the exact number of nodes you may have to look for the minimum key? (Hint: figure out where the min. key may only exist in a max-heap?) 3. A binomial heap BHresresultsfrommergingBHabovewithanothermax-heapBH1 with 2n1++2m+3 keys after two delete-max operations at BH where the maximum key is at the root of Bm and the second maximum at the root of Bn1 (i.e., first the two deletemaxs then the merging). i. How many nodes does BHres have? ii. What binomial trees is BHres composed of