Insert jquery ui datepicker in dropdown menuitem

First of all, thanks for all the answers I've already found on this forum on all sorts of programming topics. Tried to find a solution for the following problem for the last couple of hours. Hoping there's someone who knows more about the jquery UI datepicker.

I try to insert a jquery UI datepicker in a CSS dropdown menu. In a "normal" menu (menu without a submenu) the datepicker shows as expected but in the dropdown menu I get the following result: http://jsfiddle.net/h3Stj/3/

Is it impossible to nest the datepicker in two ? Is there a solution?

the html

    <div id="headtext">
    <nav id="menu-top">
        <ul class="menu-ul">
            <li id="menuitem0"><span>Menu</span>

                <ul class="submenu">
                    <li id="menuitem1"><a href="javascript:kalender();">Kalender Item</a>
                        <div id="datepicker"></div>
                        <div></div>
                    </li>
                    <li id="menuitem2"><a href="#">Menuitem 2</a>
                    </li>
                    <li id="menuitem3"><a href="#">Menuitem 3</a>
                    </li>
                </ul>
            </li>
        </ul>
    </nav>
</div>

the css

nav {
    text-align: center;
}
.menu-ul li {
    list-style: none;
    min-height: 40px;
    background-color: #d92322;
}
.menu-ul a {
    text-decoration: none;
    display: block;
    color: white;
    width: 250px;
    min-height: 40px;
    padding-top: 5px;
}
.menu-ul span {
    display: block;
    color: white;
    width: 250px;
    padding-top: 5px;
    height: 35px;
}
.submenu {
    visibility:hidden;
    position: absolute;
    float: left;
}
.menu-ul li:hover .submenu {
    visibility:visible;
}
.submenu li:hover {
    background-color: #424242;
}
.submenu li {
    border-top-style: solid;
    border-top-color: white;
    border-top-width: 2px;
}
#datepicker {
    display: block;
}
.ui-datepicker {
    width: 250px;
}

and the code

$(function() {
$( "#datepicker" ).datepicker();
});

Many thanks!