Candy Game X05322

Luke and Lucy have a new game to play. They have a large heap of candies of different types. Lucy plays first, and in each turn, a player can take one or more candies of the same type from the heap. The player who takes the last candy from the heap loses.

Who will win the game, assuming that both players play optimally?

Input

The first line of input contains a single integer N, the number of candy types (1 ≤ N ≤ 10000).

For i = 1 to N, i-th following line contains a_i, the number of candies of type i, 1 ≤ a_i ≤ 10000.

Output

Output either Lucy or Luke.