Hong likes game very much. He wants to play a game with you.

There is a tree with N nodes. Node 1 is the root. Each node is colored black or white.

Each turn, the player should choose a black node and change it to white. After that, he can choose its any number of the proper ancestors and change their color. The one who cannot find a black node at the tree in his turn, he lose the game.

Hong is good at the game, so he let you take the first turn. Hong will always find the optimal solution. He wants to know if you can win the game.