How to select open path objects not include no filled objects?

I use CS6.

I want to select open path objects, but not include no filled objects.

That means if these objects with open path and filled any color or gradient, I want to select them.

Now I can select objects with open path.

var doc = app.activeDocument;

doc.selection = null;

numClosed = 0;

for ( var i = 0; i < doc.pathItems.length; i++ )

{

    if ( ! doc.pathItems[i].closed )

    {

        doc.pathItems[i].selected = true;

        numClosed++;

    }

}

alert(numClosed + " paths open.");

But how to not include no filled shapes?

Anybody know?

Thank you.