Brito is playing with his daughter Raquel. He has n

wooden pieces, each with a number from $1$ to n$.$ Each piece also has another natural number on the back; piece i has number p$($i$).$ Raquel must count how many pairs $($i$,$j$)$ of pieces satisfies ip$($j$).$ She gets a treat if she can find them all before Brito!

Design a Divide and Conquer algorithm to determine how many pairs Raquel must find to earn her treat.

Your input is a list P$=[1...$n$]$ where entry P$[$i$]$ is the number on the back of piece i$.$ You may assume all entries of P are distinct.