WIP: Add input broadcasting and client-side prediction features

Changes include:
- Client: INPUT_BROADCAST packet handling and opponent prediction rendering
- Client: Protocol parsing for INPUT_BROADCAST packets
- Server: Input broadcasting to all clients except sender

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

server/server.py

@@ -571,6 +571,33 @@ class GameServer:
         if player_id is None:
             return
         logging.debug("INPUT from player_id=%d: %d events (base_tick=%d)", player_id, len(events), base_tick)
+
+        # Apply inputs to snake buffer (client-side filtering already applied)
+        snake = self.runtime.state.snakes.get(player_id)
+        if snake is not None:
+            for ev in events:
+                # Apply input buffer rules from project plan:
+                # - Max capacity 3
+                # - If opposite to last buffered, replace last
+                # - Drop duplicates
+                # - Overflow: replace last
+                if len(snake.input_buf) > 0:
+                    last_dir = snake.input_buf[-1]
+                    # Check if opposite (XOR == 2)
+                    if (int(ev.direction) ^ int(last_dir)) == 2:
+                        # Replace last
+                        snake.input_buf[-1] = ev.direction
+                        continue
+                    # Check if duplicate
+                    if ev.direction == last_dir:
+                        continue
+                # Add to buffer
+                if len(snake.input_buf) < 3:
+                    snake.input_buf.append(ev.direction)
+                else:
+                    # Overflow: replace last
+                    snake.input_buf[-1] = ev.direction
+
         # Relay to others immediately for prediction
         await self.relay_input_broadcast(
             from_player_id=player_id,