[SalesForce] LWC: Picklist without knowing recordTypeId

In lwc-recipes, there is a component wireGetPicklistValues explaining how to fetch picklist values. This is the code below:

import { LightningElement, wire } from 'lwc';
import { getPicklistValues } from 'lightning/uiObjectInfoApi';
import TYPE_FIELD from '@salesforce/schema/Account.Type';

export default class WireGetPicklistValues extends LightningElement {
    @wire(getPicklistValues, {
        recordTypeId: '012000000000000AAA',
        fieldApiName: TYPE_FIELD
    })
    picklistValues;
}

In the code above, recordTypeId value is hardcoded. I checked the documentation for getPicklistValues wire adapter.
https://developer.salesforce.com/docs/component-library/documentation/lwc/lwc.reference_wire_adapters_picklist_values

It's mentioned that to get recordTypeId, use the Object Info defaultRecordTypeId property, which is returned from getObjectInfo or getRecordUi.

So I modified my code as below, but it's still giving me runtime exception. Can anyone point me out where am I wrong?

import { LightningElement, wire, track } from 'lwc';
import { getPicklistValues } from 'lightning/uiObjectInfoApi';
import TYPE_FIELD from '@salesforce/schema/Account.Type';

import { getObjectInfo } from 'lightning/uiObjectInfoApi';
import ACCOUNT_OBJECT from '@salesforce/schema/Account';

export default class WireGetPicklistValues extends LightningElement {
    @wire(getPicklistValues, {
        recordTypeId: this.objectInfo.data.defaultRecordTypeId,
        fieldApiName: TYPE_FIELD
    })
    picklistValues;

    @wire(getObjectInfo, { objectApiName: ACCOUNT_OBJECT })
    objectInfo;

}