Box A and box B have 6 cards each. Each card is marked with one integer, 1 through 6. Both boxes can have more than one card with the same integer, but the sum of all the integers in each box must be 18. Two of the cards in box/1 are 6's and two of the cards in box B are 5's. If one card is drawn from box A and one from box B, but neither a 6 nor a 5 is drawn, what is the largest possible sum of the integers on the cards drawn from the two boxes?