I am going on a 5 week trip to China in June, and then a week long trip to Italy this August. I was hoping to get a new camera to use while I'm away. I have a budget of around 400-700$, and was maybe considering a mirrorless camera. I want the camera to be somewhat mobile and preferably even pocket-able. Norm has raved about the NEX 3c, but how long would the battery life be. Thanks so much.