how can I restrict the top level keys of a heavily nested object?

Question

I have a nested object such as:

{ 
  'a': { 123: { 'XYZ': { name: 'thing' } } },
  'b': { 456: { 'ZZZ': { name: 'other thing' } } },
}

I want to apply restrictions such that the top level keys can only be 'a' or 'b', the 2nd level object's keys can only be numbers, the 3rd level object's keys can only be strings, and the values of that inner object is an object conforming to a specific interface.

I tried doing:

interface Item {
  id: number;
  name: string;
}
type ValidKeys = 'a' | 'b';

let items = { [index: ValidKeys] : ([index: number] : ([index : string] : Item)) } = {};

But [index: ValidKeys] is not allowed, and gives me

An index signature parameter type cannot be a literal type or generic type. Consider using a mapped object type instead.

How can I limit the allowed keys of the top level object?