Query for solr empty field

Question

I am having a list of profiles in solr, indexing with some empty fields (e.g.: country/category etc).

<arr name="country">
    <str>185</str>
</arr>
<arr name="category">
    <int>38</int>
</arr>

I want to search profiles with no country. I used -country:['' TO *] as country is a string field.

Now how can I check it for an integer field? The field may be empty (no field) or with value 0. I tried category:0 but it is not giving me the correct output, output is empty in this case.