how to filter a multilevel menu with a search input

Question

The difficulty is that the menu has many levels(like the menu in matrix-admin),and every level is large; how should i filter filter the menu on the basis of the value of the search input.

and the output should be like this:(http://www.jqueryrain.com/?lEMFOjZ1) and my html is like this:

<ul>
<li>xxx</li>
<li>
   <a>xxx</a>
   <ul>
      <li>
           <a>xxx</a>
           <ul>
                <li>
                   <a>xxx</a>
                   <ul></ul>
                </li>
           </ul>
      </li>
      <li>xxxx</li>
   </ul>
</li>

Answer 1

Demo Fiddle

$("li").each(function () {
    if (filter == "") {
        $(this).css("visibility", "visible");
        $(this).fadeIn();
    } else if ($(this).text().search(new RegExp(filter, "i")) < 0) {
        $(this).css("visibility", "hidden");
        $(this).fadeOut();
    } else {
        $(this).css("visibility", "visible");
        $(this).fadeIn();
    }
});  

Onkeypress event the menu will be filtered.... The parent li will be visible, if you try find the child li...