===== ISTEM =====
Solve the following programming task.

TASK: LRU Cache (Least Recently Used)

Write an 'LRUCache(capacity)' class with a fixed capacity. 'get(key)' must return the value (or -1 if absent) and mark that key as most recently used. 'put(key, value)' must insert or update the value; when capacity is exceeded it must evict the least recently used entry. All operations must run in average O(1) time.

STARTER CODE (python):
class LRUCache:
    def __init__(self, capacity: int):
        pass

    def get(self, key: int) -> int:
        pass

    def put(self, key: int, value: int) -> None:
        pass


RULES:
- Keep the function name and signature EXACTLY as given.
- Return working code only. No explanations.
- Put the code in a single ``` block.
- Try to solve it first. If you genuinely cannot, write only this single
  line instead of producing faulty code: CANNOT_SOLVE

===== HAM YANIT =====
```python
class LRUCache:
    class _Node:
        __slots__ = ('key', 'value', 'prev', 'next')

        def __init__(self, key=0, value=0):
            self.key = key
            self.value = value
            self.prev = None
            self.next = None

    def __init__(self, capacity: int):
        self.capacity = capacity
        self.map = {}
        # Sentinel head/tail for doubly linked list
        self.head = self._Node()
        self.tail = self._Node()
        self.head.next = self.tail
        self.tail.prev = self.head

    def _remove(self, node):
        node.prev.next = node.next
        node.next.prev = node.prev

    def _add_to_front(self, node):
        node.next = self.head.next
        node.prev = self.head
        self.head.next.prev = node
        self.head.next = node

    def get(self, key: int) -> int:
        if key not in self.map:
            return -1
        node = self.map[key]
        self._remove(node)
        self._add_to_front(node)
        return node.value

    def put(self, key: int, value: int) -> None:
        if key in self.map:
            node = self.map[key]
            node.value = value
            self._remove(node)
            self._add_to_front(node)
        else:
            if len(self.map) >= self.capacity:
                lru = self.tail.prev
                self._remove(lru)
                del self.map[lru.key]
            node = self._Node(key, value)
            self.map[key] = node
            self._add_to_front(node)
```