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You are given an array of servers represented by their processing power. You want to join consecutive servers together to form larger, more powerful servers. You can only join server i with server i+1 if the processing power of server i+1 is strictly greater than the processing power of server i. This joining process can cascade, meaning that if you join i and i+1, and the new combined processing power is less than i+2, you can then join the combined server with i+2, and so on. The goal is to maximize the number of these larger servers. For example: Consider the array [1, 2, 3, 4, 5]. You can join 1 and 2 to form 3. Then you can join 3 and 3 to form 6. Then you can join 6 and 4 to form 10. Finally, you can join 10 and 5 to form 15, resulting in one server with processing power 15. Consider the array [5, 4, 3, 2, 1]. You cannot join any servers because the processing power is always decreasing. Consider the array [1, 3, 2, 4, 1, 5]. You can join 1 and 3 to get 4. You cannot join 4 and 2. You can join 2 and 4 to get 6. You cannot join 6 and 1. You can join 1 and 5 to get 6. The final servers will be [4, 6, 6]. Write a function that takes an array of integers representing server processing powers and returns the final array of server processing powers after performing all possible joins.

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Design a Chess Board using Object-Oriented principles. Consider the classes, their attributes, and methods. Focus on the core components like the board, pieces, and interactions between them. For example, how would you represent the different chess pieces (pawn, rook, knight, etc.) and their unique movement rules? How would you handle the logic for checking if a move is valid, including considering piece-specific constraints and checking for checkmate or stalemate scenarios? Illustrate with code snippets to showcase how these objects would interact. How will you handle special moves like castling and en passant? How would you keep track of the game state and handle turn management?

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Describe a time when you and a teammate had a fundamental disagreement about a project. What was the disagreement about? How did you approach resolving the disagreement? What was the outcome, and what did you learn from the experience?