Complete the implementation of the Dictionary data structure without using built-in set or dict.

The Dictionary class must expose the following methods.

• Dictionary() constructor that takes no arguments.
• set(k, v) sets the item with key k to the value v.
• get(k) returns the value of item with key k if exist, else returns -1.
• remove(k) removes the item with key k from the dictionary if exist, else do nothing.

Remember that dictionary operations must be efficient in space and time.

The following is a usage example of the Dictionary class:

data = Dictionary()
data.set(1, 1)
data.set(2, 1)
data.set(3, 3)
data.get(2)  # Returns 1
data.get(4)  # Returns -1
data.set(3, 5)
data.set(3, 2)
data.get(3)  # Returns 2
data.remove(1)
data.get(1)  # Returns -1

Constraints

Your dictionary is expected to:

• Support up to 10^5 operations
• Keys and values are integers in the range [0, 10^9]

• Implement the methods listed above under solution.py.
• All code will be checked for readability using pylint.
• A grader is included, and all test cases must pass.
• DO NOT modify the grader!
• DO NOT use built-in set or dict!

• You can run the grader with the command python3 grader.py < test_cases/a.txt where a is the test case you want to run.
• Yo can run all test cases with the command: for f in test_cases/*.txt; do python3 grader.py < "$f"; done