Reordering fields

Hi,

I’m trying to order the checkout fields. Everything works fine except the order of the password field.

The result I get is:
1- The order of the password field is not changing.
2- I get a new field under the email field!

Code below. Any idea?
Thanks

add_filter("woocommerce_checkout_fields", "order_fields");

function order_fields($fields) {

    $order = array(
        "billing_first_name",
        "billing_last_name",
        "billing_phone",
        "billing_email",
        "account_password",
        "billing_area",
        "billing_address_type",
        "billing_building",
        "billing_room",
        "billing_notes"

    );
    foreach($order as $field)
    {
        $ordered_fields[$field] = $fields["billing"][$field];
    }

    $fields["billing"] = $ordered_fields;
    return $fields;

}

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