XML Schema - multiple child elements are possible, but have unique values

Question

So I have a "hotel" root element which contains an element "rooms". Inside the rooms element, there must be a list of present rooms:

<?xml version="1.0"?>
<h:hotel xmlns:h="hotel">
    <existingRooms>
        <room>101</room>
        <room>102</room>
        <room>201</room>
    </existingRooms>
</h:hotel>

multiple rooms with the same roomnumber should be illegal:

<?xml version="1.0"?>
<h:hotel xmlns:h="hotel">
    <existingRooms>
        <room>101</room>
        <room>102</room>
        <room>201</room>
        <room>201</room>
    </existingRooms>
</h:hotel>

When I try to do this with , the validator only accepts one room, which is obviously not my goal:

<?xml version="1.0"?>
<schema xmlns="http://www.w3.org/2001/XMLSchema"
    xmlns:h="hotel"
    targetNamespace="hotel">
    <element name="hotel">
        <complexType>
            <sequence>
                <element name="existingRooms">
                    <complexType>
                        <sequence>
                            <element name="room" type="integer" maxOccurs="unbounded"/>
                        </sequence>
                    </complexType>
                </element>
            </sequence>
        </complexType>
        <unique name="inuqueRoomNumber">
            <selector xpath="existingRooms"/>
            <field xpath="room"/> 
        </unique>
    </element>
</schema>

What can be the solution for this issue?

Answer 1

Change

    <unique name="inuqueRoomNumber">
        <selector xpath="existingRooms"/>
        <field xpath="room"/> 
    </unique>

to

    <unique name="inuqueRoomNumber">
        <selector xpath="existingRooms/room"/>
        <field xpath="."/> 
    </unique>