Deep Copy Nested List

Create a deep copy of a 2D list without using copy module. The checker prints your copy and then whether it is genuinely independent — equal to the original while sharing none of its rows. Returning the original list will not pass.

Your task

Implement this function:

def deep_copy_2d(matrix: list) -> list:

Write the function only — the arguments are read for you and the return value is printed automatically.

Arguments arrive as one Python literal per line, in this order: matrix.

Example

Input

[[1, 2], [3, 4]]

Output

[[1, 2], [3, 4]]
independent copy: True