How to filter a four dimensional array in Javascript

Question

I have the following array:

[
    {
        "type": "great-grandparent",
        "value": "senior one",
        "grandparents": [
            {
                "value": "special grandparent",
                "parents": [
                    {
                        "value": "special parent",
                        "children": [
                            {
                                "value": "special child 1"
                            },
                            {
                                "value": "special child 2"
                            }
                        ]
                    },
                    {
                        "value": "special parent 256",
                        "children": []
                    }
                ]
            },
            {
                "value": "special grandparent 2",
                "parents": [
                    {
                        "value": "happy parent",
                        "children": [
                            {
                                "value": "fluffy child 1"
                            },
                            {
                                "value": "chilled child 2"
                            }
                        ]
                    },
                    {
                        "value": "special parent 242",
                        "children": []
                    }
                ]
            }
        ]
    },
    {
        "type": "great-grandparent 2",
        "value": "the other senior one",
        "grandparents": [
            {
                "value": "special grandparent 2",
                "parents": [
                    {
                        "value": "special parent 2",
                        "children": [
                            {
                                "value": "peculiar child 1"
                            },
                            {
                                "value": "curious child 2"
                            }
                        ]
                    },
                    {
                        "value": "special parent 3",
                        "children": []
                    }
                ]
            },
            {
                "value": "special grandparent 3",
                "parents": [
                    {
                        "value": "happy parent",
                        "children": [
                            {
                                "value": "fast child 1"
                            },
                            {
                                "value": "talkative child 2"
                            }
                        ]
                    },
                    {
                        "value": "special parent 4",
                        "children": []
                    }
                ]
            }
        ]
    },
    {
        "type": "great-grandparent 3",
        "value": "the other slightly senior one",
        "grandparents": [
            {
                "value": "special grandparent 67",
                "parents": [
                    {
                        "value": "special parent 243",
                        "children": []
                    },
                    {
                        "value": "special parent 34554",
                        "children": []
                    }
                ]
            },
            {
                "value": "special grandparent 345",
                "parents": [
                    {
                        "value": "extremely happy parent"
                    },
                    {
                        "value": "special parent 454",
                        "children": []
                    }
                ]
            }
        ]
    }
]

I am trying to return a nested array of great-grandparent (containing grandparent, parent and child arrays/objects) objects where children is not an empty array.

So given the above array, I expect an array of 2 elements to be returned with special parent 256, 242, 3, and 4 omitted as they have zero children. The last great-grandparent object has zero children so this great-grandparent object should be completely omitted too

So far I have:

const filtered = greatGrandparents
.filter((greatGrandparentObj) => greatGrandparentObj.grandparents
  .filter((grandparentObj) => grandparentObj.parents
    .filter((parentObj) => parentObj.children.length !== 0).length).length)

I am getting the expected greatGrandparent objects back but I am also getting back parents with zero children, I want these to be omitted.

Appreciate any guidance