# Y-game

Willy and Benny enjoy very much playing Y-game! This is a game in which white and black tokens are placed on a triangular n-grid, n ≥ 0, where n is called the order of the grid. A 3-grid is depicted in the figure below: In general, an n-grid has (n + 2)(n + 1)/2 points with nonnegative “baricentric coordinates” (x, y, z), where x + y + z = n. Coordinates in a n-grid are assigned in such way that along right to left paths x-coodinates are constant, y-coordinates increase by one unit, and z-coordinates decrease by one unit (observe that this construction maintains x + y + z = n true). Symmetric situations may be observed for left to right (where y-coordinates are constant) and horizontal (where z-coordinates are constant) paths. A point (x,y,z) in a n-grid is said to lay on the x side (resp., y side, z side) if and only if x = 0 (resp., y = 0, z = 0). Willy uses white tokens and Benny uses black ones. Y-game rules are rather complicated, but the end of the game is attained when there is a token placed on every node of the grid. The winner is that player that has formed a Y, that is, his/her tokens are so placed that they include a connected set of points with a point on each side. For example, the following figure represents an end situation where Benny wins: The winner is rather easy to determine when the grid is small. But Willy and Benny are not interested in that discussion today. Actually, they just want a software solution that computes the winner of ended Y -games. Could you help them? Input The problem input consists of several cases. A case begins with a line with two integer numbers, n and m, where n is the order of the grid and m the number of positions that have a black-coloured token (Benny’s tokens), with 0 ≤ n ≤ 20 and 0 ≤ m ≤ (n + 2)(n + 1)/2.

2/2 Then, m lines follow, each one with 3 values x, y and z representing coordinate (x,y,z) of a point in the n-grid with a black token. Values on each input line are separated by one or more spaces. The end of the input is signaled by a line 00 Output Output texts for each input case are presented in the same order that the input is read. For an input case in the puzzle statement, the output should be a single line with the left-justified text Willy or Benny accordingly to the fact that Willy or, respectively, Benny wins in that case. Sample Input 35 012 102 300 111 120 23 002 101 020 11 100 00 Sample Output Benny Willy Willy