## Task

Create a function that given a sequence of strings, groups the elements that can be obtained by rotating others, ignoring upper or lower cases. 

In the event that an element appears more than once in the input sequence, only one of them will be taken into account for the result, discarding the rest. 

## Input

Sequence of strings. Valid characters for those strings are uppercase and lowercase characters from the alphabet and whitespaces.

## Output

Sequence of elements. Each element is the group of inputs that can be obtained by rotating the strings. 

Sort the elements of each group alphabetically. 

Sort the groups descendingly by size and in the case of a tie, by the first element of the group alphabetically.

## Examples

```python
['Tokyo', 'London', 'Rome', 'Donlon', 'Kyoto', 'Paris', 'Okyot'] --> [['Kyoto', 'Okyot', 'Tokyo'], ['Donlon', 'London'], ['Paris'], ['Rome']]

['Rome', 'Rome', 'Rome', 'Donlon', 'London'] --> [['Donlon', 'London'], ['Rome']]

[] --> []
```

Difficulty: EASY
Starter code: def group_cities(seq):
	

Solutions:
def group_cities(seq):
	result = []
	sort_result = []
	seq = list(dict.fromkeys(seq))
	for (e, i) in enumerate(seq):
		sort_result = [j for j in seq if len(j) == len(i) and j.lower() in 2 * i.lower()]
		if not sorted(sort_result) in result:
			result.append(sorted(sort_result))
	return sorted(sorted(result), key=len, reverse=True)


from collections import Counter, defaultdict

def group_cities(seq):
	bases = defaultdict(lambda : defaultdict(list))
	for W in set(seq):
		w = W.lower()
		d = bases[frozenset(Counter(w).items())]
		k = next((w2 for w2 in d if w in w2), w * 2)
		d[k].append(W)
	return sorted([sorted(lst) for d in bases.values() for lst in d.values()], key=lambda g: (-len(g), g[0]))


from collections import deque

def group_cities(seq):
	result = []
	seq = sorted(set(seq))
	simples = [c.lower() for c in seq]
	skip = set()
	for (i, c1) in enumerate(simples):
		if i in skip:
			continue
		city_match = [i]
		skip.add(i)
		rolls = []
		roller = deque(c1)
		roller.rotate(1)
		while ''.join(roller) != c1:
			rolls.append(''.join(roller))
			roller.rotate(1)
		for roll in rolls:
			for (j, c2) in enumerate(simples[i + 1:], i + 1):
				if j in skip:
					continue
				if c2 == roll:
					skip.add(j)
					city_match.append(j)
		result.append(sorted([seq[k] for k in city_match]))
	result.sort(key=lambda a: (-len(a), a[0]))
	return result


def group_cities(seq):
	res = {}
	for w in seq:
		temp = [str(w[i:] + w[:i]).title() for i in range(1, len(w)) if str(w[i:] + w[:i]).title() in seq]
		temp.append(w)
		res[frozenset(temp)] = sorted(set(temp))
	return sorted(res.values(), key=lambda x: (-len(x), x[0]))


def is_palindrome(a, b):
	if len(a) != len(b):
		return False
	else:
		for i in range(1, len(a)):
			if a.lower()[i:] + a.lower()[:i] == b.lower():
				return True
		return False

def group_cities(seq):
	ans = []
	already_chosen = []
	for term in seq:
		if term not in already_chosen:
			temp = [term]
			already_chosen.append(term)
			for thing in seq:
				if thing not in already_chosen and thing != term and is_palindrome(thing, term):
					temp.append(thing)
					already_chosen.append(thing)
			ans.append(temp)
	for thing in ans:
		thing.sort()
	ans.sort(key=lambda x: x[0])
	ans.sort(key=len, reverse=True)
	return ans


from collections import defaultdict

def key(s):
	s = s.lower().replace(' ', '')
	return min((s[i:] + s[:i] for i in range(len(s))))

def group_cities(seq):
	result = defaultdict(list)
	for city in set(seq):
		result[key(city)].append(city)
	for cities in result.values():
		cities.sort()
	return sorted(result.values(), key=lambda cities: (-len(cities), cities[0]))


def group_cities(seq):
	result = []
	for element in sorted(list(dict.fromkeys(seq)), key=str.lower):
		for group in result:
			if element.lower() in [group[0].lower()[r:] + group[0].lower()[:r] for r in range(len(group[0].lower()))]:
				group.append(element)
				break
		else:
			result.append([element])
	return sorted(result, key=len, reverse=True)


from collections import deque
from operator import itemgetter

def group_cities(seq):
	seq_by_length = {}
	for s in seq:
		l = len(s)
		if l in seq_by_length:
			seq_by_length[l].append(s)
		else:
			seq_by_length[l] = [s]
	groups = []
	for elems in seq_by_length.values():
		to_check = deque(set(elems))
		while to_check:
			cur_check = to_check.pop()
			(group, check) = ([cur_check], cur_check.lower() * 2)
			for c in to_check.copy():
				if c.lower() in check:
					group.append(c)
					to_check.remove(c)
			groups.append(sorted(group))
	return sorted(sorted(groups, key=itemgetter(0)), key=len, reverse=True)


from collections import defaultdict

def group_cities(l):

	def make_key(s):
		return min((s[-i:] + s[:-i] for i in range(len(s))))
	d = defaultdict(list)
	for item in sorted(set(l)):
		d[make_key(item.lower())].append(item)
	return sorted(d.values(), key=len, reverse=True)


from collections import defaultdict

def group_cities(seq):
	key = lambda s: min((s[i:] + s[:i] for i in range(len(s))))
	d = defaultdict(set)
	for e in seq:
		d[key(e.lower())].add(e)
	return sorted((sorted(v) for v in d.values()), key=lambda x: (-len(x), x))