Error with type cast while deserializing XML using xsd.exe generated schema

I have a simple XML:

<?xml version="1.0" encoding="utf-8"?>
<room>
  <item type="computer">
    <x-coord>1</x-coord>
    <y-coord>2</y-coord>
  </item>
  <item type="chair">
    <x-coord>4</x-coord>
    <y-coord>5</y-coord>
  </item>
</room>

And I've generated XML Schema for it, as follows:

<?xml version="1.0" encoding="utf-8"?>
<xs:schema id="room" xmlns="" xmlns:xs="http://ift.tt/tphNwY" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
  <xs:element name="room" msdata:IsDataSet="true" msdata:Locale="en-US">
    <xs:complexType>
      <xs:choice minOccurs="0" maxOccurs="unbounded">
        <xs:element name="item">
          <xs:complexType>
            <xs:sequence>
              <xs:element name="x-coord" type="xs:string" minOccurs="0" msdata:Ordinal="0" />
              <xs:element name="y-coord" type="xs:string" minOccurs="0" msdata:Ordinal="1" />
            </xs:sequence>
            <xs:attribute name="type" type="xs:string" />
          </xs:complexType>
        </xs:element>
      </xs:choice>
    </xs:complexType>
  </xs:element>
</xs:schema>

Because I want my x-coord and y-coord fields to hold an Integer value, I've changed xs:string to xs:int, like this:

<xs:element name="x-coord" type="xs:int" minOccurs="0" msdata:Ordinal="0" />
<xs:element name="y-coord" type="xs:int" minOccurs="0" msdata:Ordinal="1" />

I've read somewhere that this should hold Int32 value, so I've changed my generated Room.cs to have:

 [System.Xml.Serialization.XmlElementAttribute("y-coord", Form=System.Xml.Schema.XmlSchemaForm.Unqualified)]
    public System.Int32 ycoord
    {
        get {
            return this.ycoordField;
        }
        set {
            this.ycoordField = value;
        }
    }

for both x and y coordinate. However, I still have an error with Strong Types and Cast Exception:

+       _x_coord    '(new System.Linq.SystemCore_EnumerableDebugView<NA2.room.itemRow>(this.Items.tableitem)).Items[0]._x_coord' threw an exception of type 'System.Data.StrongTypingException' int {System.Data.StrongTypingException}

+       base    {System.Data.StrongTypingException: The value for column 'x-coord' in table 'item' is DBNull. ---> System.InvalidCastException: Specified cast is not valid.

It only works with xs:string and public String ycoord. Only then the values are stored without any error but it is not what I want.

Do you know where is the problem here?