class defaultdict(dict):
    def __init__(self, default_factory=None, *args, **kwargs):
        super().__init__(*args,**kwargs)
        self.default_factory = default_factory
    def __missing__(self, key):
        if not self.default_factory: raise KeyError(key)
        let result = self.default_factory()
        self.__set__(key, result)
        return result
    def __get__(self, key):
        if key not in self:
            return self.__missing__(key)
        return super().__get__(key)

class deque():
    def __init__(self, iterable=None, maxlen=None):
        self._head = None
        self._tail = None
        self._size = 0
        self.__inrepr = False
        self.maxlen = maxlen
        if iterable:
            for i in iterable:
                self.append(i)
    def __len__(self):
        return self._size
    def append(self, item):
        if not self._head:
            let ref = [None, item, None]
            self._head = ref
            self._tail = ref
        else:
            let ref = [self._tail, item, None]
            self._tail[2] = ref
            self._tail = ref
        if self._size == self.maxlen:
            self.popleft()
            return
        self._size += 1
    def appendleft(self, item):
        if not self._head:
            let ref = [None, item, None]
            self._head = ref
            self._tail = ref
        else:
            let ref = [None, item, self._head]
            self._head[0] = ref
            self._head = ref
        if self._size == self.maxlen:
            self.pop()
            return
        self._size += 1
    def count(self, x):
        let counter = 0
        let ptr = self._head
        while ptr != None:
            if ptr[1] == x: counter++
            ptr = ptr[2]
        return counter
    def extend(self, iterable):
        for i in iterable:
            self.append(i)
    def extendleft(self, iterable):
        for i in iterable:
            self.appendleft(i)
    def index(self, x, start=None, stop=None):
        let i = 0
        let ptr = self._head
        while ptr != None:
            if ptr[1] == x and (start == None or i >= start) and (stop == None or i < stop):
                return i
            i++
            ptr = ptr[2]
        raise ValueError("value not found")
    def insert(self, i, x):
        if self._size == self.maxlen:
            raise IndexError('attempt to grow bounded deque beyond bound')
        let c = 0
        let ptr = self._head
        while ptr != None:
            if c == i:
                let l = ptr[0]
                let r = ptr[2]
                if l == None:
                    return self.extendleft(x)
                else if r == None:
                    return self.extend(x)
                let ref = [l, x, r]
                l[2] = ref
                r[0] = ref
                self._size += 1
                return
            i++
        raise IndexError("invalid insertion index")
    def pop(self):
        if not self._tail:
            raise IndexError("pop from empty deque")
        let item = self._tail[1]
        self._tail = self._tail[0]
        self._size--
        if self._tail:
            self._tail[2] = None
        return item
    def popleft(self):
        if not self._head:
            raise IndexError("pop from empty deque")
        let item = self._head[1]
        self._head = self._head[2]
        self._size--
        if self._head:
            self._head[0] = None
        return item
    def remove(self, value):
        let ptr = self._head
        while ptr:
            if ptr[1] == value:
                if ptr == self._head:
                    self._head = self._head[2]
                    if self._head:
                        self._head[0] = None
                else if ptr == self._tail:
                    self._tail = self._tail[0]
                    if self._tail:
                        self._tail[2] = None
                else:
                    let l = ptr[0]
                    let r = ptr[2]
                    if l: l[2] = r
                    if r: r[0] = l
                return
        raise ValueError("value not found")
    def rotate(self, n=1):
        if n == 0 or self._size == 0: return
        if n > 0:
            while n > 0:
                self.appendleft(self.pop())
                n--
        while n < 0:
            self.append(self.popleft())
            n++
    def reverse(self):
        if not self._head: return None
        let ptr = self._head
        self._head = self._tail
        self._tail = ptr
        while ptr:
            let l = ptr[0]
            let r = ptr[2]
            ptr[2] = l
            ptr[0] = r
            ptr = r
        return None
    def __repr__(self):
        if self.__inrepr: return 'deque(...)'
        self.__inrepr = True
        let out = 'deque(['
        let ptr = self._head
        while ptr:
            out += repr(ptr[1])
            ptr = ptr[2]
            if ptr:
                out += ', '
        out += '])'
        self.__inrepr = False
        return out
    def __str__(self):
        return repr(self)
    def __iter__(self):
        let s = self._head
        def _():
            if not s: return _
            let out = s[1]
            s = s[2]
            return out
        return _
    def __get__(self, index):
        if index >= self._size or index < -self._size: raise IndexError("Invalid index")
        if index == 0: return self._head[1]
        if index > 0:
            let ptr = self._head
            while ptr:
                if index == 0: return ptr[1]
                index--
                ptr = ptr[2]
        else:
            index = -(index + 1)
            let ptr = self._tail
            while ptr:
                if index == 0: return ptr[1]
                index--
                ptr = ptr[0]
        raise IndexError("This probably shouldn't happen?")
    def __contains__(self, value):
        if not self._head: return False
        let ptr = self._head
        while ptr:
            if ptr[1] == value: return True
            ptr = ptr[2]
        return False