Regex is behaving lazy, should be greedy

I thought that by default my Regex would exhibit the greedy behavior that I want, but it is not in the following code:

 Regex keywords = new Regex(@"in|int|into|internal|interface");
 var targets = keywords.ToString().Split('|');
 foreach (string t in targets)
    {
    Match match = keywords.Match(t);
    Console.WriteLine("Matched {0,-9} with {1}", t, match.Value);
    }

Output:

Matched in        with in
Matched int       with in
Matched into      with in
Matched internal  with in
Matched interface with in

Now I realize that I could get it to work for this small example if I simply sorted the keywords by length descending, but

• I want to understand why this isn't working as expected, and
• the actual project I am working on has many more words in the Regex and it is important to keep them in alphabetical order.

So my question is: Why is this being lazy and how do I fix it?

Laziness and greediness applies to quantifiers only (?, *, +, {min,max}). Alternations always match in order and try the first possible match.