validation rule for 2d array laravel

I have some input fields in view blade with name for example

cat[1][0],cat[1][1],cat[2][1] etc .

Now I want to write some validation rules in server side so that each input field is not empty and maximum length of text is 50.

I am facing problem writing the rule for 2d array as name. What I am doing is as below.

    $InputsWithtwoDarrayName = $request->cat;
    $rules = [];
    foreach ($InputsWithtwoDarrayName as $firstKey => $InputsWithtwoDarrayName) 
     {
        foreach ($catQuestion as $secondkey => $qstion)
            $rules['cat.' . $firstKey . '.' . $secondkey] = 'required|max:' . 50;
    }

    $messages = [
        'required' => Lang::get('message.assessment.selfAssessment.selfconfirm.error.required'),
    ];
    $validator = Validator::make($InputsWithtwoDarrayName, $rules,$messages); 
    if ($validator->fails()) {
        return Redirect::back();
    }

Now my question is what is the proper way of writing rule for 2d array as name?

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