Candy Game

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.

Problem information

Author: Eryk Kopczynski

Generation: 2026-01-25T13:24:20.364Z

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