Nimble

Each turn slides one coin left along numbered squares, so print which player moves the last coin onto square zero under optimal play.

Medium6Game theoryBit manipulationNo attempts yetTime limit2sMemory limit512 MB

Problem

Nimble is a game played on a 1×N1 \times N rectangle. The rectangle is divided into 1×11 \times 1 squares. The leftmost square is number 0, the square to its right is number 1, and so on until the rightmost square, number N1N-1. Coins sit on the squares, and one square can hold two or more coins.

Two players take turns. On a turn a player picks one coin and moves it left by at least one square. A coin cannot move past square 0.

The game ends once every coin is on square 0, and the player who moves the last coin onto square 0 wins.

koosaga and cubelover play Nimble. koosaga moves first. Print the player who wins when both play optimally.

Input

The first line contains the number of coins MM (1M1001 \le M \le 100).

The second line contains the numbers of the squares holding the coins, P1,P2,,PMP_1, P_2, \dots, P_M, separated by spaces (1Pi1091 \le P_i \le 10^9).

The rectangle is always 1×10101 \times 10^{10}.

Output

Print koosaga if koosaga wins, or cubelover if cubelover wins.