LINQ – Full Outer Join

I have a list of people’s ID and their first name, and a list of people’s ID and their surname. Some people don’t have a first name and some don’t have a surname; I’d like to do a full outer join on the two lists.

So the following lists:

ID  FirstName
--  ---------
 1  John
 2  Sue

ID  LastName
--  --------
 1  Doe
 3  Smith

Should produce:

ID  FirstName  LastName
--  ---------  --------
 1  John       Doe
 2  Sue
 3             Smith

I’m new to LINQ (so forgive me if I’m being lame) and have found quite a few solutions for ‘LINQ Outer Joins’ which all look quite similar, but really seem to be left outer joins.

My attempts so far go something like this:

private void OuterJoinTest()
{
    List<FirstName> firstNames = new List<FirstName>();
    firstNames.Add(new FirstName { ID = 1, Name = "John" });
    firstNames.Add(new FirstName { ID = 2, Name = "Sue" });

    List<LastName> lastNames = new List<LastName>();
    lastNames.Add(new LastName { ID = 1, Name = "Doe" });
    lastNames.Add(new LastName { ID = 3, Name = "Smith" });

    var outerJoin = from first in firstNames
        join last in lastNames
        on first.ID equals last.ID
        into temp
        from last in temp.DefaultIfEmpty()
        select new
        {
            id = first != null ? first.ID : last.ID,
            firstname = first != null ? first.Name : string.Empty,
            surname = last != null ? last.Name : string.Empty
        };
    }
}

public class FirstName
{
    public int ID;

    public string Name;
}

public class LastName
{
    public int ID;

    public string Name;
}

But this returns:

ID  FirstName  LastName
--  ---------  --------
 1  John       Doe
 2  Sue

What am I doing wrong?