Consider the Boolean matrix method for constructing universal hash functions. Suppose that there are 16 buckets and keys are of 6 bits. b. Consider two specific hash functions in this set: h1 containing all zeros, and h2 containing all ones.

i. Every hash function has an input set of elements on which it performs badly by mapping all the elements to the same slot. Find the largest such input set for h1. Repeat for h2.

ii. On how many key values do the hash functions h1 and h2 collide? Explain.