In the documentation (https://sdk.vercel.ai/examples/next-pages/chat/stream-chat-completion) the server code is

import { CoreMessage, streamText } from 'ai';
import { openai } from '@ai-sdk/openai';

export async function POST(req: Request) {
  const { messages }: { messages: CoreMessage[] } = await req.json();

  const result = await streamText({
    model: openai('gpt-4'),
    system: 'You are a helpful assistant.',
    messages,
  });

  return result.toDataStreamResponse();
}

I copied and pasted it into /pages/api/chat directory and the streaming fails.

Failed to load resource: the server responded with a status of 404 (Not Found)Understand this error
index.mjs:914


POST http://localhost:3000/api/chat 404 (Not Found)

I am not sure what to do