Albert, Charles and Mary invented a new version of the classical game Bingo. In traditional Bingo the game is presided over by a non-player known as the caller. In the beginning of the game each player is given a card containing a unique combination of numbers from 0 to N arranged in columns and rows. The caller has a bag containing N+1 balls, numbered from 0 to N. On each turn, the caller randomly selects a ball from the bag, announces the number of the drawn ball to the players, and sets the ball aside so that it cannot be selected again. Each player searches his/her card for the called number and marks it if he/she finds it. The first player who marks a complete pre-announced pattern on the card (for example, a full horizontal line) wins a prize.
In the Albert-Charles-Mary version, on each turn, the caller draws a first ball, returns it to the bag, draws a second ball, returns it to the bag, and then calls out the absolute difference between the two ball numbers. To generate even more excitement, before the game started a possibly empty subset of balls is removed from the bag, in such a way that at least two balls remain there. They would like to know if every number from 0 to N may still be called out with the new drawing method considering the balls that were left in the bag.
For each test case, print a single line containing a single uppercase ‘Y’ if it is possible to call out every number from 0 to N, inclusive, or a single uppercase ‘N’ otherwise.