What am I missing?

My code is here, but I cannot pass this assertion.

break_rings(((1,3),(3,4),(3,5),(4,6),(6,7),(8,3),(8,1),(2,6),(8,4),(9,5),(4,5),(1,7),))

My answer is 5, but my result is 6. I guess I miss some conditions.

def find_the_nuisance(box):
    max_len=0
    max_len_num=0
    for k, v in box.iteritems():
        if max(max_len, len(v)) == len(v):
            max_len=len(v)
            max_len_num=k
    if max_len == 0:
        return 0
    else:
        return max_len_num

def break_the_chain(nuisance, box):
    if nuisance == 0:
        return False
    else:
        friend=[]
        friend=box.pop(nuisance)
        #print friend
        for n in friend:
            box[n].remove(nuisance)
        print box
        return True


def break_rings(rings):
    import collections
    box=collections.defaultdict(list)
    for ring in rings:
        x, y = ring
        box[x].append(y) 
        box[y].append(x)
    print box
    boool=True
    count=0
    while boool:
        nuisance = find_the_nuisance(box)
        print nuisance
        boool = break_the_chain(nuisance, box)
        count+=1 
    return count-1

Would you please some pieces of advice? Thank you.