WooCommerce - Add cat ids to product page body classes

<?php
// add category identifiers in the body classes for product pages
add_filter( 'body_class', 'add_body_classes' );
function add_body_classes( $classes ) {
  global $post;
  // product pages only
  if ( is_product() ) {
    // get the categories for this product
    $terms = get_the_terms( $post->ID, 'product_cat' );
    foreach ($terms as $term) {
      // you can use either slug or id, no point having both
      $classes[] = 'cat_slug_'.$term->slug;
      $classes[] = 'cat_id_'.$term->term_id;
    }
    return $classes;
  }
}