Design a data structure that tracks the frequency of string keys and allows for efficient updates and queries.

Implement the AllOne class with these methods:

• Constructor: Initializes the data structure.

• inc(String key): Increases the count of the given key by $1$. If the key is absent, insert it with a count of $1$.

• dec(String key): Decreases the count of the given key by $1$. If the count becomes $0$ after decrementing, remove the key entirely. The assumption is that the key exists when this function is called.

• getMaxKey(): Returns any one key with the highest count. If the data structure is empty, return an empty string.

• getMinKey(): Returns any one key with the lowest count. If the data structure is empty, return an empty string.

Note: All operations must be performed in average $O(1)$ time complexity.

Constraints:

• $1 \leq$ key.length $\leq 10$

• key consists only of lowercase English letters.

• It is guaranteed that each call to dec is made with a key that exists in the data structure.

• At most $5 \times 10^2$ calls will be made to inc, dec, getMaxKey, and getMinKey.