Autosubmit multiple checkboxes as comma separated string in url?

I've looked through some topics but they either have auto-submit where each checkbox is as a separate parameter in the URL or they need submit button. What I am trying to achieve is:

My current HTML form:

<form name="status" id="status" method="get">
    <input type="checkbox" name="status[]" value="0" onchange="document.getElementById('status').submit()" />
    <input type="checkbox" name="status[]" value="1" onchange="document.getElementById('status').submit()" />
    <input type="checkbox" name="status[]" value="2" onchange="document.getElementById('status').submit()" />

With this, I have auto-submit whenever a checkbox is checked, but I have an URL like ...&status%5B%5D=0&status%5B%5D=1

What I need is a comma-separated parameter in the URL like &status=0,1 while keeping the auto-submit option. Also, there are some more parameters in the URL, so this must be appended at the end while keeping the rest parameters.

Is this possible? I'm not familiar with javascript but I think there might be a way ...

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