Implement a Batch Image Processor

Implement a program that applies basic image transformations to a batch of images. You are given a list of input image paths and, for each image, a sequence of operations to apply in order. Support the following operations: 1. **grayscale**: convert the image to grayscale. 2. **scale(factor)**: multiply both width and height by a positive floating-point scale factor. 3. **resize(width, height)**: resize the image to the exact target dimensions. ### Part 1 Write a function that processes a small batch of images correctly and saves the transformed results. Example function shape: `process_images(tasks: list[ImageTask], output_dir: str) -> list[str]` Where each `ImageTask` contains: - `input_path`: path to the source image - `operations`: ordered list of operations such as `grayscale`, `scale(0.5)`, or `resize(200, 300)` The function should return the output paths in the same order as the input tasks. ### Part 2 Now assume the images are very large and the batch size is also large. The interviewer asks you to improve performance on a multi-core machine. Update your approach so that: - multiple images can be processed in parallel, - output ordering is preserved, - a failure in one task does not corrupt other results, - the design is appropriate for CPU-heavy image processing. You may use a standard Python imaging library such as Pillow.