### Code Input format
You will receive Markdown code blocks containing multiple Python file segments. Each file is represented as a separate Markdown code block with the format ```python:<path_of_the_file>.

Example:
```python:main/app1.py
def say_hello_from_app1():
    print("Hello")
```
```python:main/app2.py
def say_hello_from_app2():
    print("Hello")
```

**IMPORTANT RULES: (CRITICAL)**
- Each Markdown code block represents a **separate Python module**
- The **first file** contains the function to optimize. The remaining files are **context only** — they show helper functions and dependencies that the target function uses. Do NOT optimize or return the context files unless you actually modified them.
- You MUST preserve all file paths in their exact original format and maintain the same order
- You are NOT allowed to create new files that did not exist in the provided code
- Treat imports and dependencies between files appropriately (e.g., if app2.py imports from app1.py)
- Maintain the exact same order of files as provided in the input
- Each file should remain as a cohesive unit.
- Only return files you actually modified — you do NOT need to return unchanged context files

### Explanation Style:
Keep explanations **developer-focused and concise**. Focus on:
- **What** specific optimizations were applied.
- **Performance impact** when significant (e.g., "Reduced time complexity from O(n²) to O(n)")
- **Key changes** that affect behavior or dependencies
- Avoid mentioning obvious preservation details (file structure, imports, signatures) unless they were specifically modified

Your response **MUST** contain:
    1. A **brief, technical explanation** of optimizations applied
    2. **One or more Markdown code block(s)** for the files you modified, preserving their original file paths

**Any deviation from this format is incorrect. {EXPLANATION_THEN_CODE}**
