Aggregation sum in Spring Data MongoDB

I have MongoDB Page and Post collections. Each page document has field postIds which is array of post Ids (String objects). I want to use aggregation to count number of posts (=number of elements in array postIds) for each page. I wrote Mongo Shell aggregation function which returns exactly what I want:

db.page.aggregate([
    {$unwind : '$postIds'},
    {$group : {_id: '$_id', 'sum': { $sum: 1}}}
])

and it returns this result:

{ "_id" : "3", "sum" : 3 }
{ "_id" : "2", "sum" : 3 }

This means that page with id 3 has 3 posts, and page with id 2 has 3 posts as well, which is correct.

Now I wanted to write same using Spring MongoDB Aggregation, and wrote this simple JUnit test:

    /**
     * Test page posts count
     */
    @Test
    public void testPagePostsCount() throws Exception{
        MongoTemplate template = repository.getMongoTemplate();
        Page page = new Page();
        page.setPageId("2210");
        page.setUserId("azec");
        List<String> postList = new ArrayList<String>();
        postList.add("53eb1a560efbe048c7ea698d");
        postList.add("53eb1a6b0efbe048c7ea698e");
        page.setPostIds(postList);
        template.save(page);

        Aggregation agg = newAggregation(
            match(Criteria.where("pageId").is("2210")),
            unwind("postIds"),
            group("_id").sum("1").as("sum")
            //project("$sum").and("pageId").previousOperation()
        );

        AggregationResults<PostCount> results = template.aggregate(agg, "page", PostCount.class);
        List<PostCount> postCount = results.getMappedResults();

        System.out.println("Done!");
    }

However, this aggregation query returns this native Mongo query:

2014-08-13 20:06:07,949 DEBUG [org.springframework.data.mongodb.core.MongoTemplate] - Executing aggregation:

{
   "aggregate":"page",
   "pipeline":[
      {
         "$match":{
            "pageId":"2210"
         }
      },
      {
         "$unwind":"$postIds"
      },
      {
         "$group":{
            "_id":"$_id",
            "sum":{
               "$sum":"$1"
            }
         }
      }
   ]
}

Questions: 1. As you can see, the difference is with the $sum value of $1. I need to pass there number 1 instead of $1, but I am not sure how. 2. Do I need project operation here?

Thanks