class Node:
    def __init__(self, key, value):
        self.key = key
        self.value = value
        self.prev = None
        self.nxt = None

class NodeList:
    def __init__(self):
        self.size = 0
        self.head = None
        self.tail = None

    def insert(self, node):
        if node is None:
            return
        self.size += 1
        if self.size == 1:
            self.head = node
            self.tail = node
        else:
            node.nxt = self.head
            self.head.prev = node
            self.head = node

    def remove(self, node):
        if node is None:
            return
        self.size -= 1

        if self.head == node:
            self.head = node.nxt
        if self.tail == node:
            self.tail = node.prev

        if node.prev is not None:
            node.prev.nxt = node.nxt
        if node.nxt is not None:
            node.nxt.prev = node.prev

        node.prev = None
        node.nxt = None