A and B play a dice game using two dice namely 'X' and 'Y'. The numbers inscribed on the six faces of 'X' are 1, 2, 3, 4, 5 and 7, and the numbers
inscribed on the six faces of 'Y' are 2, 3, 4, 5, 6 and 8. In each round of the game, each players rolls both the dice simultaneously and records the product of the two numbers appearing on the top of the two dice as his scores for that round. In a particular round, the sum of the scores of A and B is an even number, then how many distinct scores A could have had in that round?