Please generate a unique JSON object suitable for automating the programming task testing platform, strictly in the following format:
    {
  "Title": "Task Name",
  "Task Description": "Description of the task.",
  "Function Signature": "def function_name(parameters) -> return_type:",
  "Solve": "",
  "Input": "Description of the input parameters.",
  "Output": "Description of the expected output.",
  "Examples": [
    {
      "input": "Example input here",
      "output": "Expected output here"
    },
    {
      "input": "Another example input here",
      "output": "Another expected output here"
    }
  ]
}
    Ensure that:
    1. The task includes complex sorting algorithms.
    2. The JSON follows this exact structure and does not include any additional text or variations.
    3. The task should be complex and unique, avoiding direct copying from common platforms like LeetCode or similar sources.
    4. The solution must not use any imports in the code (i.e., no import statements).
    5. The 'Solve' section must remain empty.
    6. Ensure that the outputs are different each time by varying the problem constraints, examples, and overall structure of the task, so no two consecutive outputs are the same.
    7. Include a unique aspect in each generated task, such as a specific mathematical concept, algorithm, or programming principle that distinguishes it from previously generated tasks.
    8. The 'Function Signature' should strictly follow the format: 'def function_name(parameters) -> return_type:', but the 'Solve' section must remain empty. Ensure that the input description corresponds to the expected parameters in the signature.
    
Ensure that the solution must not be any of the following titles:
- Reverse and Count Vowels
- Custom Merge Sort with Inversion Count
- Find Shortest Path in Weighted Graph
- Count Unique Paths in a Grid
- Longest Increasing Subsequence with Constraints
- Determine DNA Base Pairing
- String Transformation and Analysis
- Fraction Simplification
- Matrix Spiral Traversal
- Custom Radix Sort for Positive Integers
- String Compression with Patterns
- Maximal Subarray Sum with Constraints
- Character Frequency Analysis
- String Palindrome and Anagram Checker
- Nested List Sum with Depth Weighting
- Nested List Product with Depth Weighting
- Character Frequency Rearrangement
- Optimized Binary Search with Nested Structures
- Custom Bucket Sort with Range Constraints
- Graph Colorability Checker
- Optimized Dynamic Programming with Duplicates
- Nested Dictionary Value Aggregation
- Custom Quick Sort with Median of Medians
- Nested List Depth Average
- Advanced K-way Merge Sort
- Optimal Coin Change with Limited Supply
- Optimized Merge Sort with Arbitrary Sort Criteria
- Hierarchical Employee Salary Calculation
- Custom Heap Sort with Priority Levels
- String Pattern Replacer
- String Rotation and Count Unique Characters
- Custom Heap Sort with Dynamic Priority Adjustment
- Pattern Removal from String
- Maximum Product Subarray with Constraints
- Minimize Cost of Coin Change with Constraints
- String Interleaving with Constraints
- Frequency-Preserving Rearrangement
- Nested Fibonacci Sequence Sum
- Unique Graph Path
- Mixed Case Word Transposition
- Graph Connectivity and Cycle Detection
- String Reversal and Character Mapping
- Longest Palindromic Subsequence with Constraints
- Custom Heap Sort with Dynamic Element Prioritization
- Graph Traversal with Unique Path Counting
- Optimal Subset Sum with Constraints
- Hierarchical Data Aggregation
- Nested Palindrome Checker
- Minimal Spanning Tree and Minimum Path Finding
- Optimal Task Assignment with Constraints
- Finding Path with Maximum Sum in Weighted Digraph
- Balanced Partition Problem
- Optimal Word Break with Constraints
- Component Counting in Nested Structures
- Custom Graph Traversal with Unique Node Counting
- Nested JSON Object Comparison
- Unique Graph Traversal with Distance Calculation
- Nested JSON Object Flattener
- Optimal Subarray Product with Constraints
- Dynamic Programming for Nested Matrices
- Nested Prime Factorization
- Hierarchical Data Retrieval with Filtering
- String Sequence Transformation
- Nested Tuple Comparison
- Substring Frequency Analysis
- Optimal Job Scheduling with Constraints
- Cyclic String Manipulation
- Dynamic Programming with Modular Arithmetic
- Cyclic String Shift and Count
- Nested List Sum with Dynamic Depth Weights
- Custom Matrix Rotation with Layer Tracking
- Optimal Path Through a Triangular Grid
- Graph Traversal for Unique Destination Count
- Optimal Palindrome Partitioning with Constraints
- String Manipulation with Unique Character Count
- Optimal Subsequence Sum with Constraints
- String Manipulation with Unique Character Frequency
- Nested Array Product with Depth Weighting
- Dynamic Programming with Range Constraints
- Optimal Path in a 3D Grid with Obstacles
- Custom Sort with Frequency and Order Preservation
- Unique Graph Traversal with Distance Tracking
- Custom String Encoding with Unique Patterns
- Graph Traversal for Maximum Edge Weight Path
- Dynamic Programming for Mixed Integer Knapsack
- Custom Sorting with Weighted Priorities
- Custom Sort Based on Frequency and Value
- Advanced String Manipulation with Substitution
- Dynamic Programming with Unique Path Counting
- Maximum Sum of Non-Adjacent Elements with Constraints
- Multi-Faceted Sorting Algorithm Application
- Graph Traversal with Unique Node Visits
- String Manipulation with Unique Character Grouping
- Cyclic String Transformation with Unique Character Shift
- Weighted Graph Traversal for Resource Allocation
- Advanced Sorting with Custom Criteria
- Nested List Max Product
- Nested List Element Frequency
- Optimal Subsequence Product with Constraints
- Unique Palindromic Number Repetition Identification
- Dynamic Programming with String Transposition
- Nested Dictionary Value Merger
- Cyclic Character Shift and Count
- Nested Array Element Frequency
- Hierarchical Data Structure Flattener
- Custom Sorting with Prime Number Criteria
- Dynamic Programming with Unique Compositions
- Advanced Sorting with Custom Key Function
- Three-level Nested List Maximum Sum
- Graph Traversal with Minimum Edge Weight Path
- String Manipulation with Unique Character Grouping
- Custom Sorting with Geometric Progression Criteria
- Optimized Dynamic Programming with Unique Path Counting
- Custom Sorting with Geometric Progression Criteria
- Advanced Sorting with Commutative Property
- Graph Traversal with Unique Path Length Calculation
- Custom Sorting with Fibonacci Sequence Criteria
- Nested Palindrome Product Finder
- Optimal Subset Selection with Constraints
- String Compression with Character Frequency
- Graph Traversal with Unique Path Counting
- Route Planner with Harvesting Constraints
- Optimal Knapsack Selection with Unique Weights
- Optimized Binary Search with Unique Comparison Function
- Unique Island Count
- Graph Traversal for Unique Path Lengths
- String Manipulation with Unique Character Frequency
- Embossed Pattern Counter
- Graph Traversal for Unique Path Lengths
- Optimal Path in a Hexagonal Grid
- Advanced Nested Matrix Manipulation
- Custom Sorting with Exponential Growth Criteria
- Minimize Cost of Path Selection with Constraints
- String Manipulation with Unique Character Grouping
- Advanced String Transformation with Replacements
- Custom Sorting with Product Magnitude
- Nested Array Element Frequency Analysis
- String Sequence Analyzer
- Cyclic String Transformation with Unique Character Shift
- Graph Traversal with Unique Path Length Calculation
- Nested Array Element Frequency Analysis
- Hierarchical Tree Depth Sum
- Unique Character Substring Finder
- String Manipulation with Unique Character Grouping
- Custom Sorting with Geometric Series Criteria
- String Pattern Transformation with Unique Mapping
- Nested List Character Frequency
- Graph Traversal for Unique Path Discovery
- Graph Traversal with Unique Path Length Calculation
- Nested List Maximum Depth Product
- Custom Sorting with Geometric Progression Criteria
- Graph Traversal with Unique Path Length Calculation
- Graph Traversal for Unique Path Discovery
- String Manipulation with Unique Character Encoding
- Graph Traversal for Longest Path in Directed Acyclic Graph
- Nested Array Maximum Depth Product
- Graph Traversal for Unique Node Pair Count
- String Transformation with Unique Character Mapping
- Custom Sorting with Prime Factorization Criteria
- Custom Sorting with Custom Weighting
- Optimal Subarray Sum with Unique Constraints
- Graph Traversal for Unique Node Pair Count
- Nested Matrix Diagonal Sum
- String Manipulation with Unique Character Encoding
- Optimal Path in a Hexagonal Grid with Obstacles
- Maximal Rectangle Area in Binary Matrix
- Unique Graph Path with Weight Constraints
- Custom Sorting with Prime Factor Count
- Graph Traversal for Unique Node Pair Count
- Cyclic String Reversal and Substring Search
- Unique Character Sequence Manipulation
- Maximum Length of Non-Overlapping Subarrays
- Optimal Resource Allocation with Constraints
- Nested Palindrome Substring Finder
- Graph Traversal for Unique Component Counting
- Custom Sorting with Modular Arithmetic Criteria