How can I mount Cloudflare Durable Objects to a route?

import { Hono } from 'hono'

export default class Counter {
  value: number = 0
  state: DurableObjectState
  app: Hono = new Hono()

  constructor(state: DurableObjectState) {
    this.state = state
    this.state.blockConcurrencyWhile(async () => {
      const stored = await this.state.storage?.get<number>('value')
      this.value = stored || 0
    })

    this.app.get('/increment', async (c) => {
      const currentValue = ++this.value
      await this.state.storage?.put('value', this.value)
      return c.text(currentValue.toString())
    })

    this.app.get('/decrement', async (c) => {
      const currentValue = --this.value
      await this.state.storage?.put('value', this.value)
      return c.text(currentValue.toString())
    })

    this.app.get('/', async (c) => {
      return c.text(this.value.toString())
    })
  }

  async fetch(request: Request) {
    return this.app.fetch(request)
  }
}

import { Hono } from 'hono'

export default class Counter {
  value: number = 0
  state: DurableObjectState
  app: Hono = new Hono()

  constructor(state: DurableObjectState) {
    this.state = state
    this.state.blockConcurrencyWhile(async () => {
      const stored = await this.state.storage?.get<number>('value')
      this.value = stored || 0
    })

    this.app.get('/increment', async (c) => {
      const currentValue = ++this.value
      await this.state.storage?.put('value', this.value)
      return c.text(currentValue.toString())
    })

    this.app.get('/decrement', async (c) => {
      const currentValue = --this.value
      await this.state.storage?.put('value', this.value)
      return c.text(currentValue.toString())
    })

    this.app.get('/', async (c) => {
      return c.text(this.value.toString())
    })
  }

  async fetch(request: Request) {
    return this.app.fetch(request)
  }
}

import durableObject from "./durable-object";

export const app = new Hono();
app.route("/durable-object", durableObject);

import durableObject from "./durable-object";

export const app = new Hono();
app.route("/durable-object", durableObject);

Argument of type 'typeof Counter' is not assignable to parameter of type 'Hono<Env, Schema, string>'.
  Type 'typeof Counter' is missing the following properties from type 'Hono<Env, Schema, string>': #private, get, post, put, and 25 more.ts(2345)
⚠ Error (TS2345)  | 
Argument of type 
 is not assignable to parameter of type 
 .
   

Type 
 is missing the following properties from type 
 :
#private, get, post, put, and 25 more.

Argument of type 'typeof Counter' is not assignable to parameter of type 'Hono<Env, Schema, string>'.
  Type 'typeof Counter' is missing the following properties from type 'Hono<Env, Schema, string>': #private, get, post, put, and 25 more.ts(2345)
⚠ Error (TS2345)  | 
Argument of type 
 is not assignable to parameter of type 
 .
   

Type 
 is missing the following properties from type 
 :
#private, get, post, put, and 25 more.