Where can I extend the input type for trpc router?

const recaptchaMiddleware = t.middleware(async ({ next, ctx, input }) => {
  if (Object.keys(input ?? {}).includes("recaptchaToken")) {
    const res = await fetch("https://www.google.com/recaptcha/api/siteverify", {
      method: "POST",
      headers: {
        "Content-Type": "application/x-www-form-urlencoded",
      },
      body: new URLSearchParams({
        secret: process.env.RECAPTCHA_SECRET_KEY ?? "",
        response: (input as { [key: string]: unknown; recaptchaToken: string })
          .recaptchaToken,
      }),
    });
    if (!res.ok) {
      throw new Error("Failed to verify reCAPTCHA token");
    }
    const data = (await res.json()) as {
      success: true | false; // whether this request was a valid reCAPTCHA token for your site
      score: number; // the score for this request (0.0 - 1.0)
      action: string; // the action name for this request (important to verify)
      challenge_ts: string; // timestamp of the challenge load (ISO format yyyy-MM-dd'T'HH:mm:ssZZ)
      hostname: string; // the hostname of the site where the reCAPTCHA was solved
      "error-codes": string[] | undefined; // error codes if the request failed
    };
    if (!data.success) {
      throw new Error("reCAPTCHA verification failed");
    }
    if (data.score < 0.5) {
      throw new Error("reCAPTCHA score too low");
    }
  }
  return next({
    ctx: {
      ...ctx,
      recaptcha: {
        verified: true,
      },
    },
  });
});

const recaptchaMiddleware = t.middleware(async ({ next, ctx, input }) => {
  if (Object.keys(input ?? {}).includes("recaptchaToken")) {
    const res = await fetch("https://www.google.com/recaptcha/api/siteverify", {
      method: "POST",
      headers: {
        "Content-Type": "application/x-www-form-urlencoded",
      },
      body: new URLSearchParams({
        secret: process.env.RECAPTCHA_SECRET_KEY ?? "",
        response: (input as { [key: string]: unknown; recaptchaToken: string })
          .recaptchaToken,
      }),
    });
    if (!res.ok) {
      throw new Error("Failed to verify reCAPTCHA token");
    }
    const data = (await res.json()) as {
      success: true | false; // whether this request was a valid reCAPTCHA token for your site
      score: number; // the score for this request (0.0 - 1.0)
      action: string; // the action name for this request (important to verify)
      challenge_ts: string; // timestamp of the challenge load (ISO format yyyy-MM-dd'T'HH:mm:ssZZ)
      hostname: string; // the hostname of the site where the reCAPTCHA was solved
      "error-codes": string[] | undefined; // error codes if the request failed
    };
    if (!data.success) {
      throw new Error("reCAPTCHA verification failed");
    }
    if (data.score < 0.5) {
      throw new Error("reCAPTCHA score too low");
    }
  }
  return next({
    ctx: {
      ...ctx,
      recaptcha: {
        verified: true,
      },
    },
  });
});