Notification Feed

Build a notification feed component in React with TypeScript. The component polls a simulated API every 5 seconds to check for new notifications. Each notification has an id, message, timestamp, and read boolean.

The feed displays all notifications sorted by timestamp (newest first) and shows a count of unread notifications at the top. Users can mark individual notifications as read by clicking them.

Simulate the API by generating a random notification with Math.random() on each poll (50% chance of a new notification appearing).

Output

Produce TypeScript/TSX files in a src/ directory:

• src/types.ts -- TypeScript type definitions
• src/components/NotificationFeed.tsx -- the main feed component with polling and unread count
• src/components/NotificationItem.tsx -- component for a single notification

Do not include test files or build configuration.