# class _LinkedListNode:
#     def __init__(self, prev, next, value) -> None:
#         self.prev = prev
#         self.next = next
#         self.value = value

# class deque:
#     def __init__(self, iterable=None) -> None:
#         self.head = _LinkedListNode(None, None, None)
#         self.tail = _LinkedListNode(None, None, None)
#         self.head.next = self.tail
#         self.tail.prev = self.head
#         self.size = 0
#         if iterable is not None:
#             for value in iterable:
#                 self.append(value)

#     def __getitem__(self, index):
#         assert 0 <= index < len(self)
#         node = self.head.next
#         for _ in range(index):
#             node = node.next
#         return node.value
    
#     def __setitem__(self, index, value):
#         assert 0 <= index < len(self)
#         node = self.head.next
#         for _ in range(index):
#             node = node.next
#         node.value = value

#     def __delitem__(self, index):
#         assert 0 <= index < len(self)
#         node = self.head.next
#         for _ in range(index):
#             node = node.next
#         node.prev.next = node.next
#         node.next.prev = node.prev
#         self.size -= 1

#     def clear(self):
#         self.head.next = self.tail
#         self.tail.prev = self.head
#         self.size = 0

#     def extend(self, iterable):
#         for value in iterable:
#             self.append(value)

#     def append(self, value):
#         node = _LinkedListNode(self.tail.prev, self.tail, value)
#         self.tail.prev.next = node
#         self.tail.prev = node
#         self.size += 1
    
#     def appendleft(self, value):
#         node = _LinkedListNode(self.head, self.head.next, value)
#         self.head.next.prev = node
#         self.head.next = node
#         self.size += 1

#     def pop(self):
#         assert self.size > 0
#         node = self.tail.prev
#         node.prev.next = self.tail
#         self.tail.prev = node.prev
#         self.size -= 1
#         return node.value
    
#     def popleft(self):
#         assert self.size > 0
#         node = self.head.next
#         node.next.prev = self.head
#         self.head.next = node.next
#         self.size -= 1
#         return node.value
    
#     def copy(self):
#         new_list = deque()
#         for value in self:
#             new_list.append(value)
#         return new_list
    
#     def __len__(self):
#         return self.size
    
#     def __iter__(self):
#         node = self.head.next
#         while node is not self.tail:
#             yield node.value
#             node = node.next

#     def __repr__(self) -> str:
#         a = list(self)
#         return f"deque({a})"
    
#     def __eq__(self, __o: object) -> bool:
#         if not isinstance(__o, deque):
#             return False
#         if len(self) != len(__o):
#             return False
#         t1, t2 = self.head.next, __o.head.next
#         while t1 is not self.tail:
#             if t1.value != t2.value:
#                 return False
#             t1, t2 = t1.next, t2.next
#         return True

def Counter(iterable):
    a = {}
    for x in iterable:
        if x in a:
            a[x] += 1
        else:
            a[x] = 1
    return a

class defaultdict:
    def __init__(self, default_factory) -> None:
        self.default_factory = default_factory
        self._a = {}

    def __getitem__(self, key):
        if key not in self._a:
            self._a[key] = self.default_factory()
        return self._a[key]
        
    def __setitem__(self, key, value):
        self._a[key] = value

    def __repr__(self) -> str:
        return f"defaultdict({self.default_factory}, {self._a})"
    
    def __eq__(self, __o: object) -> bool:
        if not isinstance(__o, defaultdict):
            return False
        if self.default_factory != __o.default_factory:
            return False
        return self._a == __o._a
    
    def __iter__(self):
        return iter(self._a)

    def __contains__(self, key):
        return key in self._a
    
    def __len__(self):
        return len(self._a)

    def keys(self):
        return self._a.keys()
    
    def values(self):
        return self._a.values()
    
    def items(self):
        return self._a.items()

    def pop(self, *args):
        return self._a.pop(*args)