Bipartite Graphs and Matchings · Easy problem

Six people $1,2,\dots,6$ are friends as follows: $1,2,3$ are mutual friends (every pair of them is a friendship), and in addition $3$ and $4$ are friends, $4$ and $5$ are friends, and $5$ and $6$ are friends. What is the maximum number of disjoint friend-pairs that can be matched up for a project, each person joining at most one pair?