Traffic Jam

Luke and Lucy are caught in a traffic jam, and they are bored, so they create a new game to play. The board is a street divided into small cells, numbered from 1. Some cars are standing on the street.

Lucy plays first, and in each turn, a player can take one car and moves it toward 1. A car cannot stand in a place where another car already is, and cannot jump over other cars. The player who makes the last move (after which cars are standing in positions $1, 2, \ldots, N$ ) wins.

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 cars ( $1 \leq N \leq 10000$ ).

For $i$ = 1 to $N$ , $i$ -th following line contains $a_i$ , the number of the cell where $i$ -th car is standing, $1 \leq a_1 \leq a_2 \cdots a_N \leq 100000000$ .

Output

Output either Lucy or Luke.

Problem information

Author: Eryk Kopczynski

Generation: 2026-01-25T13:24:30.492Z