Search box as a menu item in the nav menu output by wp_nav_menu?

based on : http://wpfirstaid.com/2010/10/extend-the-wordpress-menu/

function wpa_58902($items){
    $search="<li class="search">";
    $search .= '<form method="get" id="searchform" action="https://wordpress.stackexchange.com/">';
    $search .= '<label for="s" class="assistive-text">Search</label>';
    $search .= '<input type="text" class="field" name="s" id="s" placeholder="Search" />';
    $search .= '<input type="submit" class="submit" name="submit" id="searchsubmit" value="Search" />';
    $search .= '</form>';
    $search .= '</li>';

    return $items . $search;
}
add_filter('wp_nav_menu_items','wpa_58902');