I wonder if anyone who owns one of these (27, 32 or 37-inch) can answer the following, as it's not entirely clear from the manual: 1. Are the picture settings "per input" - in other words does it remember separate settings for each input? 2. Also, does it remember which input you were on when it was switched off so that it comes back up on the same input when switched on? 3. Did anyone ever finally establish whether the 27" model was 1280x720 or 1366x768? Thanks for any answers.