Bucket$-$sort: You are given an array A of n random integers in the range $[1...$r$]$ as input. The output data consists of r buckets, such that at the end of the algorithm, Bucket i contains indices of all the elements in A that are equal to i$.$

Describe a decomposition based on partitioning the input data $($i$.$e$.,$ the array A$)$ and an appropriate mapping onto p processes. Describe briefly how the resulting parallel algorithm would work.

Describe a decomposition based on partitioning the output data $($i$.$e$.,$ the set of r buckets$)$ and an appropriate mapping onto p processes. Describe briefly how the resulting parallel algorithm would work.