def transitive_cloure(array):

    new_list = [set(array.pop(0))]  # initialize first set with value of index `0`

    for item in array:
        for i, s in enumerate(new_list):
            if any(x in s for x in item):
                new_list[i] = new_list[i].union(item)
                break
        else:
            new_list.append(set(item))
    return new_list


def countGroups(arr):

    inp = [list(x) for x in arr]
    size = len(inp)
    relationships = []

    for i in range(size):
        for j in range(size):
            if (inp[i][j] == '1'):
                if ((i,j) not in relationships) and ((j,i) not in relationships):
                    relationships.append((i,j))
                if i != j:
                    if (i, i) in relationships:
                        relationships.remove((i, i))
                    if (j, j) in relationships:
                        relationships.remove((j, j))

#     to_remove_elts = []
#     for (i, j) in relationships:
#         if i != j: # it is already part of a couple
#             to_remove_elts.append((i, i))
#             to_remove_elts.append((j, j))

#     for item in to_remove_elts:
#         if item in relationships:
#             relationships.remove(item)

    transitive_relationships = transitive_cloure(relationships)
    return len(transitive_relationships)