Datepicker icon does not appear next to input textbox

Question

As you can see on the following JS Fiddle, I can only get the small Datepicker Icon to appear next to one of the input boxes. I need it to appear next to both.

However, changing 'id' to 'class' doesn't work, and results in both icons disappearing.

http://jsfiddle.net/Vzt39/

HTML:

           <title>jQuery UI Datepicker - Icon trigger</title>

      <script src="//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>

    <script src="//ajax.googleapis.com/ajax/libs/jqueryui/1.10.3/jquery-ui.min.js"></script>


      <script src="http://code.jquery.com/jquery-1.9.1.js"></script>
      <script src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>

      <script>
      $(function() {
        $( "#datepicker" ).datepicker({
          showOn: "button",
          buttonImage: "calendar.gif",
          buttonImageOnly: true
        });
      });
      </script>



    <p>Date: <input type="text"  id="datepicker" /></p>
     <p>Date: <input type="text" id="datepicker" /></p>


CSS:


  <link rel="stylesheet" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />


  <link rel="stylesheet" href="/resources/demos/style.css" />

Answer 1

  <script>
  $(function() {
    $( "#datepicker" ).datepicker({
      showOn: "button",
      buttonImage: "calendar.gif",
      buttonImageOnly: true
    });
      $( "#datepicker2" ).datepicker({
      showOn: "button",
      buttonImage: "calendar.gif",
      buttonImageOnly: true
    });    
  });
  </script>