title: MongoD size of multiple nested arrays
body: <p>I have collection of poems. The document in the collection has the following structure:</p>
  
  <pre><code>{
  "_id" : "Romeo and Juliet",
  "acts" : [ 
      {
          "title" : "ACT I",
          "scenes" : [ 
              {
                  "title" : "SCENE I. Verona. A public place.",
                  "action" : [ 
                      {
                          "character" : "SAMPSON",
                          "says" : [ 
                              "Gregory, o' my word, we'll not carry coals."
                          ]
                      }, 
                      {
                          "character" : "GREGORY",
                          "says" : [ 
                              "No, for then we should be colliers."
                          ]
                      }, 
                      // ...
                      {
                          "character" : "GREGORY",
                          "says" : [ 
                              "To move is to stir; and to be valiant is to stand:", 
                              "therefore, if thou art moved, thou runn'st away."
                          ]
                      }, 
                      {
                          "character" : "SAMPSON",
                          "says" : [ 
                              "A dog of that house shall move me to stand: I will", 
                              "take the wall of any man or maid of Montague's."
                          ]
                      }, 
                      {
                          "character" : "GREGORY",
                          "says" : [ 
                              "That shows thee a weak slave; for the weakest goes", 
                              "to the wall."
                          ]
                      }
                      // ...
                  ]
              }
              // ...
          ]
      }
      // ...
  ]}  
  </code></pre>
  
  <p>I want to count number of acts and scenes for each poem.
  I tried to do something like this, but the result is incorrect. </p>
  
  <pre><code>db.poems.aggregate([{$unwind:"$acts"}, {$unwind:"$acts.scenes"}, {$group: {_id: "$_id", pa: {$push: {poemAct:"$acts"}}, ps: {$push: {poemScenes:"$acts.scenes"}}}}, {$project: {numberOfActs: {$size: "$pa"}, numberOfScenes: {$size: "$ps"}}}]).pretty()
  </code></pre>
  
  <p>Help somebody, please :D</p>