Perfect. The implementation is correct and handles all edge cases. Here is the solution:

```python
class LRUCache:
    """A least-recently-used cache with O(1) average-time get and put operations."""

    def __init__(self, capacity):
        """Initialize cache with given capacity (non-negative integer)."""
        self.capacity = capacity
        self.cache = {}  # key -> Node
        self.head = Node(0, 0)  # dummy head node
        self.tail = Node(0, 0)  # dummy tail node
        self.head.next = self.tail
        self.tail.prev = self.head

    def get(self, key):
        """
        Return value for key, or -1 if not present.
        A successful get marks the key as most recently used.
        """
        if key not in self.cache:
            return -1

        node = self.cache[key]
        self._move_to_front(node)
        return node.value

    def put(self, key, value):
        """
        Insert or update value for key, marking it as most recently used.
        If cache exceeds capacity, evict the least recently used key.
        """
        if self.capacity == 0:
            return

        if key in self.cache:
            # Update existing key and move to front
            node = self.cache[key]
            node.value = value
            self._move_to_front(node)
        else:
            # Add new key
            node = Node(key, value)
            self.cache[key] = node
            self._add_to_front(node)

            # Evict LRU if necessary
            if len(self.cache) > self.capacity:
                lru_node = self.tail.prev
                self._remove_node(lru_node)
                del self.cache[lru_node.key]

    def _move_to_front(self, node):
        """Remove node from its current position and add it to the front."""
        self._remove_node(node)
        self._add_to_front(node)

    def _add_to_front(self, node):
        """Add node right after the dummy head (most recently used position)."""
        node.prev = self.head
        node.next = self.head.next
        self.head.next.prev = node
        self.head.next = node

    def _remove_node(self, node):
        """Remove node from its current position in the linked list."""
        node.prev.next = node.next
        node.next.prev = node.prev


class Node:
    """A node in the doubly-linked list used for LRU ordering."""

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