사용자 이름 가용성 확인을 위해 jQuery Validate의 원격 방법을 사용하는 방법은 무엇입니까?

$("#signupForm").validate({
    rules: {
        username: {
            required: true,
            minlength: 3,
            remote: "check-username.php"
        }
    },
    messages: {
        username: {
            remote: "This username is already taken! Try another."
        }
    }
});

<?php
require_once "./source/includes/data.php";
header('Content-type: application/json');

$name = mysql_real_escape_string($_POST['username']);

$check_for_username = mysql_query("SELECT username FROM mmh_user_info WHERE username='$name'");

if (mysql_num_rows($check_for_username) > 0) {
    $output = true;
} else {
    $output = false;
}
echo json_encode($output);
?>

require_once "./source/includes/data.php";
header('Content-type: application/json');
$request = $_REQUEST['username'];

$query = mysql_query("SELECT * FROM mmh_user_info WHERE username ='$username'");
$result = mysql_num_rows($query);
if ($result == 0){
$valid = 'true';}
else{
$valid = 'false';
}
echo $valid;
?>