datepicker applies to wrong field

I'm facing a little problem with my jQuery UI datepicker. The thing is, I have my page and some input like this :

blabla | blabla | .date-picker | blabla
blabla2 | blabla2 | .date-picker | blabla2
blabla3 | blabla3 | .date-picker | blabla3

So the 'blabla' are just some text, and the '.date-picker' is an input, with the 'date-picker' class.

In my JavaScript code I have just the following :

$(function() {
    $('.date-picker').datepicker();
});

But for example, if I click on the input of the line "blabla3", instead of updating the right input, it always updates the first one...

My input have all the same id (I can't change it), but I'm using the class of the input for my selector, so it should work but doesn't.