How to add country drop down menu to the user profile?

I've added this code snippet to my functions.php

function my_new_contactmethods( $contactmethods ) {  
    $contactmethods['country'] = 'country';
    return $contactmethods;
}
add_filter('user_contactmethods','my_new_contactmethods',10,1);

It works perfactly as I wanted. It show an extra field to fill up user country on user backend profile.

But it just a text field. Actually I want to show this field as a drop down menu which has all the countries.

How can I modify this code to get a country list dropdown menu ?