Of eight bags, numbered 1 to 8 and each containing 100 coins, six contain gold coins (a real gold coin weighs 10 grams) and two contain counterfeit coins, indistinguishable from the real ones except for their mass. The counterfeit coins in one bag weigh 11 grams each, and the counterfeit coins in the other bag weigh 12 grams. You have a graduated scale that can weigh any mass up to 10 kg to the nearest gram. You must determine, in a single weighing and by taking the fewest possible coins from each bag, which bag contains the 11-gram coins and which bag contains the 12-gram coins.

What will be the sum, in grams, of the 56 distinct masses that can be read on the scale?*