How to transform a JSON with Jolt?

Question

I have a json which contains categories and subcategories, I would like to transform it using Jolt.

Thereof:

[
    {
        "id": 1,
        "name": "Alimentos",
        "children": [
            {
                "id": 2,
                "name": "Arroz"
            },
            {
                "id": 3,
                "name": "Azeites"
            }
        ]
    },
    {
        "id": 4,
        "name": "Beleza e Higiene",
        "children": [
            {
                "id": 5,
                "name": "Óleos essenciais"
            },
            {
                "id": 6,
                "name": "Sabonetes"
            }
        ]
    }
]

For that reason:

[
    {
        "id": 1,
        "name": "Alimentos",
        "parent_id": 0
    },
    {
        "id": 2,
        "name": "Arroz",
        "parent_id": 1
    },
    {
        "id": 3,
        "name": "Azeites",
        "parent_id": 1
    },
    {
        "id": 4,
        "name": "Beleza e Higiene",
        "parent_id": 0
    },
    {
        "id": 5,
        "name": "Óleos essenciais",
        "parent_id": 4
    },
    {
        "id": 6,
        "name": "Sabonetes",
        "parent_id": 4
    }
]

Trying:

[
  {
    "operation": "shift",
    "spec": {
      "*": {
        "id": "categories.@(1,id).category_id",
        "name": "categories.@(1,id).name",
        "children": {
          "*": {
            "id": "categories.@(1,id).category_id",
            "name": "categories.@(1,id).name"
          }
        }
      }
    }
  }
]