Min Heap Class

Implement a class `MinHeap` that mimics a minimum priority queue. The class must have the following methods: - `push(value)`: Add an integer `value` to the heap. - `pop()`: Remove and return the smallest element currently in the heap. If the heap is empty, return `None`. - `peek()`: Return the smallest element without removing it. If the heap is empty, return `None`. - `size()`: Return the number of elements currently in the heap. Your implementation must maintain the heap property: after every push or pop, every parent must be less than or equal to its children. You may implement the heap as a list and perform standard heap operations (bubble-up and bubble-down). Do not use Python's built-in `heapq` module; implement the logic yourself. You are also required to implement a helper function `push_pop_order(values: list) -> list` that takes a list of integers, pushes them all into a `MinHeap` instance, then pops all elements one by one and returns the resulting list (should be sorted ascending). Similarly, implement: - `peek_empty() -> None` (return the result of calling `peek()` on an empty heap) - `pop_empty() -> None` - `size_after_operations(ops: list) -> int` where `ops` is a list of integers; push each integer, then pop once, and return the final size. - `peek_after_push(value: int) -> int` (push the value and return the result of `peek()`). Make sure these functions use your `MinHeap` class and are defined in the starter code. The class definition and method signatures are given. Implement them inside the provided class and implement the helper functions as described. Your code will be tested with a series of method calls and helper function calls, and the results must match the expected order.

>>> h = MinHeap()
>>> h.push(5)
>>> h.push(3)
>>> h.push(8)
>>> h.peek()
3
>>> h.pop()
3
>>> h.pop()
5
>>> h.size()
1
>>> push_pop_order([5,3,8,1])
[1,3,5,8]
>>> peek_after_push(7)
7
>>> size_after_operations([1,2,3])
2