"""O(1) Least-Frequently-Used cache.

Design: each frequency bucket is a doubly-linked list ordered by recency
(most-recently-used at the head). A node stores key, value, freq. On access
the node moves from its current bucket to the next-frequency bucket's head.
min_freq tracks the bucket containing the least-frequent (and among those,
least-recently-used) node for O(1) eviction.
"""


class _Node:
    __slots__ = ("key", "value", "freq", "prev", "next")

    def __init__(self, key, value):
        self.key = key
        self.value = value
        self.freq = 1
        self.prev = None
        self.next = None


class _DLList:
    """Doubly linked list with sentinel head/tail; most-recent at head side."""

    __slots__ = ("head", "tail", "size")

    def __init__(self):
        self.head = _Node(None, None)  # sentinel
        self.tail = _Node(None, None)  # sentinel
        self.head.next = self.tail
        self.tail.prev = self.head
        self.size = 0

    def add_front(self, node):
        node.prev = self.head
        node.next = self.head.next
        self.head.next.prev = node
        self.head.next = node
        self.size += 1

    def remove(self, node):
        node.prev.next = node.next
        node.next.prev = node.prev
        node.prev = None
        node.next = None
        self.size -= 1

    def pop_tail(self):
        # least recent = node before tail sentinel
        if self.size == 0:
            return None
        node = self.tail.prev
        self.remove(node)
        return node

    def is_empty(self):
        return self.size == 0


class LFUCache:
    def __init__(self, capacity):
        if capacity < 0:
            raise ValueError("capacity must be non-negative")
        self.capacity = capacity
        self._key = {}          # key -> _Node
        self._freq = {}         # freq -> _DLList
        self._min_freq = 0

    def _touch(self, node):
        # move node from its current freq bucket to freq+1 bucket head
        old_list = self._freq[node.freq]
        old_list.remove(node)
        if old_list.is_empty():
            del self._freq[node.freq]
            if self._min_freq == node.freq:
                self._min_freq += 1
        node.freq += 1
        self._freq.setdefault(node.freq, _DLList()).add_front(node)

    def get(self, key):
        if key not in self._key:
            return -1
        node = self._key[key]
        self._touch(node)
        return node.value

    def put(self, key, value):
        if self.capacity == 0:
            return
        if key in self._key:
            node = self._key[key]
            node.value = value
            self._touch(node)
            return
        # eviction if needed
        if len(self._key) >= self.capacity:
            evict_list = self._freq.get(self._min_freq)
            if evict_list is not None:
                node = evict_list.pop_tail()
                if node is not None:
                    del self._key[node.key]
                    if evict_list.is_empty():
                        del self._freq[self._min_freq]
        # insert new node at freq 1
        node = _Node(key, value)
        self._key[key] = node
        self._freq.setdefault(1, _DLList()).add_front(node)
        self._min_freq = 1