Note: This problem may be trickier and it is only worth $8$ points.

Design an algorithm that does the following: Given an input array A

of length n containing distinct positive integers, output an array B so that

B$[$i$]$ contains the number of values j in $\{0,...,$ n $1\}$ so that j $>$ i and

$3$ A$[$j$]>$ A$[$i$].$

Example: If the input is A $=[6,2,4,1,7],$ the output would be B $=$

$[2,3,1,1,0].$

Your algorithm should run in time O$($n log n$).$ If it helps, you may assume

that n is a power of $2.$

$[$We are expecting: Pseudocode, and a clear English description of what

your algorithm is doing. You do not need to justify the running time or the

correctness.$]$