How to reposition the elements of a json array conditionally using jq?

I want to re-position elements of an array (change index of array elements) based on a condition. I don't know how to translate this to jq which is more of a *functional* language. Basically I want to sort the array but the *relative* position of specific elements should be unchanged.

for each element:
if element.role==master => record type
  for each element:
    if element.type == recorded type
      reposition the element to be below its master of similar type

I can explain better with an example. Consider input.json. How can I move all non-master elements with type "x" below their masters **without** changing the **relative** position of non-master of the same type. (ignore "num" parameter. Used only for showing relativity) input.json

[
    {
        "type": "A",
        "role": "master"
    },
    {
        "num": 1,
        "type": "A"
    },
    {
        "type": "C",
        "role": "master"
    },
    {
        "num": 4,
        "type": "B"
    },
    {
        "num": 2,
        "type": "B"
    },
    {
        "type": "B",
        "role": "master"
    },
    {
        "num": 3,
        "type": "B"
    },
    {
        "num": 4,
        "type": "A"
    },
    {
        "num": 2,
        "type": "A"
    },
    {
        "num": 0,
        "type": "C"
    },
    {
        "num": 5,
        "type": "C"
    },
    {
        "num": 1,
        "type": "A"
    },
    {
        "num": 1,
        "type": "B"
    }
]

goal.json

[
    {
        "type": "A",
        "role": "master"
    },
    {
        "num": 1,
        "type": "A"
    },
    {
        "num": 4,
        "type": "A"
    },
    {
        "num": 2,
        "type": "A"
    },
    {
        "num": 1,
        "type": "A"
    },
    {
        "type": "C",
        "role": "master"
    },
    {
        "num": 0,
        "type": "C"
    },
    {
        "num": 5,
        "type": "C"
    },
    {
        "type": "B",
        "role": "master"
    },
    {
        "num": 4,
        "type": "B"
    },
    {
        "num": 2,
        "type": "B"
    },
    {
        "num": 3,
        "type": "B"
    },
    {
        "num": 1,
        "type": "B"
    }
]

As you can see: 1- The relative positions of masters is left unchanged (A - C - B) 2- The relative positions of non-masters of the same type is left unchanged. (I guess this problem has a name in algorithms literature? in-place sorting?)