def unique_combinations(number_letter_dict):
    def _unique_combinations(index):
        if index == size:
            yield ()
            return
        number, letters = number_letters[index]
        for letter in letters:
            if letter not in used_letters:
                used_letters.add(letter)
                for combination in _unique_combinations(index + 1):
                    yield [number, letter], *combination
                used_letters.remove(letter)
    number_letters = list(number_letter_dict.items())
    size = len(number_letters)
    used_letters = set()
    return list(_unique_combinations(0))
 
number_letter_dict = {1: ['a', 'b', 'c'], 2: ['c', 'd'], 3: ['b', 'c']}
print(unique_combinations(number_letter_dict))

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