class CircularQueue:
    """
    Fixed-capacity FIFO queue backed by a ring buffer.

    Parameters
    ----------
    capacity : int
        Maximum number of elements the queue can hold.
    """

    def __init__(self, capacity: int):
        if capacity < 1:
            raise ValueError("capacity must be at least 1")
        self._capacity = capacity
        self._buffer   = [None] * capacity
        self._head     = 0   # index of the front element
        self._tail     = 0   # index where the next element will be written
        self._count    = 0

    # ── Core operations ────────────────────────────────────────────────

    def enqueue(self, item):
        """Add *item* to the tail. Raises OverflowError if the queue is full."""
        if self.is_full():
            raise OverflowError("enqueue into a full circular queue")
        self._buffer[self._tail] = item
        self._tail  = (self._tail + 1) % self._capacity
        self._count += 1

    def dequeue(self):
        """Remove and return the front item. Raises IndexError if the queue is empty."""
        if self.is_empty():
            raise IndexError("dequeue from an empty circular queue")
        item = self._buffer[self._head]
        self._buffer[self._head] = None   # release reference
        self._head  = (self._head + 1) % self._capacity
        self._count -= 1
        return item

    def peek(self):
        """Return the front item without removing it. Raises IndexError if empty."""
        if self.is_empty():
            raise IndexError("peek at an empty circular queue")
        return self._buffer[self._head]

    # ── State queries ──────────────────────────────────────────────────

    def is_empty(self):
        """Return True if the queue holds no items."""
        return self._count == 0

    def is_full(self):
        """Return True if the queue has reached its capacity."""
        return self._count == self._capacity

    def size(self):
        """Return the number of items currently stored."""
        return self._count

    @property
    def capacity(self):
        """Maximum number of items the queue can hold."""
        return self._capacity

    # ── Display ────────────────────────────────────────────────────────

    def __repr__(self):
        items = []
        for i in range(self._count):
            items.append(self._buffer[(self._head + i) % self._capacity])
        return f"CircularQueue({items}, capacity={self._capacity})"

    def __str__(self):
        items = []
        for i in range(self._count):
            items.append(str(self._buffer[(self._head + i) % self._capacity]))
        return " <- ".join(items) or "(empty)"