Problem $4.[$Category: Stable matching$]$

Recall in Homework $4$ where you worked on the unhappy friends problem:

You are given a list of preferences for n friends, where n is always even. For each person i$,$ pref erences$[$i$]$

contains a list of friends sorted in the order of preference. Friends in each list are denoted by integers from $0$

to n $1.$ All the friends are divided into pairs. The pairings are given in a list pairs, where pairs$[$i$]=[$xi$,$ yi$]$

denotes xi is paired with yi and yi is paired with xi$.$

However, this pairing may cause some of the friends to be unhappy. A friend x is unhappy if x is paired

with y and there exists a friend a who is paired with b but:

x prefers a over y$,$ and a prefers x over b$.$ Return the number of unhappy friends.

Given the the preferences and pairs input like below, what$$s output $($ the count of unhappy friends$)$ will be$?$

Justify your answer briefly. $($you can run the input directly with your homework submission script.$)$

Input: n $=4,$ preferences $=[[3,2,1],[2,3,0],[1,3,0],[1,2,0]],$ pairs $=[[0,1],[2,3]]$

Output: