Multiple Datepicker elements format problem

Multiple Datepicker elements format problem

Hi

In the following code, element datepicker1 is not  initialised as per line 2 of script. But if I move line 1 after line 2, it works. Can someone please explain if this is a bug or intended behaviour.
 
<p>Date: <input type="text" id="datepicker1" name="dp"></p>
 <p>Date: <input type="text" id="datepicker2" name="dp"></p>
<p>Date: <input type="text" ></p>
   
<script>
      //line 1
      $( "input" ).datepicker(); //next line has no effect. However, if move this line after next line, it works.

      //line 2
      $( "#datepicker1" ).datepicker({changeMonth:true, changeYear:true, dateFormat:"yy-mm-dd"});
</script>