Check/uncheck input checkboxes in Isotope

I have a simple Isotope grid with checkbox inputs to sort the items in a grid. This works OK. The problem is the interaction between the "Show All" checkbox and the different category checkboxes.

When "Show All" is checked, I have to manually uncheck it to be able to check any category checkboxes. And when I uncheck all the categories, I'd like to have "Show all" check itself to indicate that all category items are being shown.

1. How can I have "Show All" uncheck itself when any one or all of the categories are checked?

2. How can I have "Show All" check itself when all of the categories are unchecked?

and

3. How can I have "Show all" be checked on page load?

https://codepen.io/bluedogranch/pen/MWvdyNm

jQuery

var $container = $('#container').isotope({
    itemSelector: '.product',
    layoutMode: 'fitRows',
    transitionDuration: '0.2s'
  });
  
  var $checkboxes = $('#filters input');
  $checkboxes.change(function(){
    var filters = [];
    // get checked checkboxes values
    $checkboxes.filter(':checked').each(function(){
      filters.push( this.value );
    });
    filters = filters.join(', ');
    $container.isotope({ filter: filters });
  });

CSS

.product  {
float: left;
width: 50px;
height: 50px;
border: 1px solid #000;
padding:10px;
text-align:center;
margin: 5px;
}

#container {
width:400px;

HTML

<div id="filters">
<label><input type="checkbox" value="*"  id="all">Show all</a></li>
<label><input type="checkbox" value=".category1" id="category1">Category 1</label>
<label><input type="checkbox" value=".category2" id="category2">Category 2</label>
<label><input type="checkbox" value=".category3" id="category3">Category 3</label>
</div>

<div id="container">

<div class="product category1">1</div>

<div class="product category1 category2 ">1,2</div>

<div class="product category1 category3">1,3</div>

<div class="product category2">2</div>

<div class="product category2 category3">2,3</div>

<div class="product category3">3</div>

<div class="product category3 category2">3,2</div>

<div class="product category1">1</div>

<div class="product category2">2</div>

<div class="product category3">3</div>

<div class="product category2">2</div>

<div class="product category1">1</div>

</div>