Dearboy is a game lover. Recently, he loves playing the game Lian Lian Kan. This game is played on a board with N*M grids, and lots of cards are put on the board in the grids. You should find a pair of the same cards, if not more than three segments can link this pair without passing any other cards, you can take this pair away from the board. (You may be puzzled about the meaning of not more than 3 segments, just refer to the figure below, in which we express some allowable links). Continue the process above, if you can clear all the cards, you win the game, otherwise you lose it.
If you have played this game, you may know that sometimes the game has no solution and you are sure to lose. Dearboy is very boring about the games without solutions, so he asks you, a famous programmer, to tell him whether he can win the giving game phase or not.