Build a Restaurant Menu API

Problem/Feature Description

A restaurant needs a Next.js App Router application to manage its menu. Build the API endpoints and a simple page to display the menu.

Endpoints:

• GET /api/menu -- list all menu items
• GET /api/menu/[id] -- get a single menu item by ID
• POST /api/menu -- create a new menu item (fields: name, description, price, category)
• PUT /api/menu/[id] -- update a menu item
• DELETE /api/menu/[id] -- delete a menu item

Business rules:

• Name is required and must be non-empty
• Price must be a positive number
• Category must be one of: appetizer, main, dessert, drink
• Menu item names must be unique

Use in-memory storage (no real database needed).

Also create a page at /menu that displays all menu items fetched from the API.

Output Specification

Produce:

• app/api/menu/route.ts -- GET and POST handlers
• app/api/menu/[id]/route.ts -- GET, PUT, DELETE handlers for single items
• app/menu/page.tsx -- server component page displaying menu items
• package.json -- with dependencies

You may create additional files as needed for a well-structured codebase.