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))



    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)