At Audible, a subscriber can gift an audiobook from his/her library to any other non-subscriber to kick start their audiobook journey. The first time subscriber can receive up to a maximum of N audiobooks from their friends/relatives. When a non-subscriber receives an audiobook, we can infer that the two may be related. Similarly, if the non-subscriber receives gifted books from two other subscribers, we can infer that all of them are related and the three of them form a group. More formally, a group is composed of all of the people who know one another, whether directly or transitively. Audible would like your help finding out the number of such distinct groups from the input data. Consider the following input matrix M:
110
110
001

Every row corresponds to a subscriber and the value M[i][j] determines if j was gifted a book by i. In the above example, user 0 has gifted a book to user 1 and so they are connected [0][1], while person 2 has not received a book from anyone or gifted book to anyone. Therefore, there are 2 groups. M[i][j] = 1 if i == j (Each of the people is known to self)

Required:
Determine the number of groups represented in a matrix.