Winner of the Bubble Game

Two players alternately swap adjacent out-of-order pairs until the permutation is sorted; the one who cannot move loses. Decide the winner.

Medium5CombinatoricsGame theoryMathNo attempts yetTime limit2sMemory limit512 MB

Problem

Andrea, Carlos and Marcelo spend every weekend at the pool. While Andrea sunbathes, the other two play a game called Bubbles. Andrea studies computer science and tells them she does not see why such a simple game takes them so long.

On Andrea's laptop the two players generate a random integer NN and a random permutation of 1,2,,N1, 2, \dots, N.

The players move in turn and Marcelo always starts.

A move is to pick a pair of consecutive elements of the sequence that are out of order and swap the two elements. For the sequence 1,5,3,4,21, 5, 3, 4, 2 a player may swap 5 and 3, or swap 4 and 2, but may not swap 3 and 4, and may not swap 5 and 2. Swapping 5 and 3 turns the sequence into 1,3,5,4,21, 3, 5, 4, 2.

Sooner or later the sequence ends up sorted in increasing order. The player who has no move on their turn loses.

Andrea says with some disdain that a coin flip would settle it just as well. Given the initial sequence, decide who wins.

Input

The input contains several test cases. Each test case is given on a single line, with the integers separated by one space. Each line starts with an integer NN (2N1052 \le N \le 10^5), followed by the initial sequence P=(X1,X2,,XN)P = (X_1, X_2, \dots, X_N) of NN pairwise distinct integers, where 1XiN1 \le X_i \le N for every ii.

The last line of the input contains a single 00.

Output

For each test case print one line holding the name of the winner, either Carlos or Marcelo, with no extra spaces.