Give custom class names to WP nav sub-menu

I was able to work this out by using a hook that I grabbed from Artemiy Egorov’s answer on this post https://stackoverflow.com/questions/5034826/wp-nav-menu-change-sub-menu-class-name so I figured I’d share in case someone else needs it too:

add_filter( 'nav_menu_submenu_css_class', 'rename_sub_menus', 10, 3 );
function rename_sub_menus( $classes, $args, $depth ){
    foreach ( $classes as $key => $class ) {
    if ( $class == 'sub-menu'  && $depth == 0) {
        $classes[ $key ] = 'first-level-sub-menu';
    } else if ( $class == 'sub-menu'  && $depth == 1) {
      $classes[ $key ] = 'second-level-sub-menu';
    } else if ( $class == 'sub-menu'  && $depth == 2) {
      $classes[ $key ] = 'third-level-sub-menu';
    }
}

return $classes;
}