Jsonpath to json schema requirement

JsonPath to json schema

I would like to generate a json schema from a list of jsonpath.

Example: 
For this kind of input,
```
$.firstName
$.lastName
$.address.streetAddress
$.address.city
$.address.postalCode
$.phoneNumbers[0].type
$.phoneNumbers[0].number
```

the result should be:
```
{
  "firstName": "John",
  "lastName" : "doe",
  "address"  : {
    "streetAddress": "",
    "city"         : "",
    "postalCode"   : ""
  },
  "phoneNumbers": [
    {
      "type"  : "",
      "number": ""
    }
  ]
}
```

From now, I don't know how can I do this... So, if someone have some kind of algorithm in mind, I'll take it :)