Nim Game 2

Two players alternately remove stones from one of N piles and the player taking the last stone wins, so decide the winner under optimal play.

Medium4Game theoryBit manipulationNo attempts yetTime limit2sMemory limit512 MB

Description

Examples8

Problem

koosaga and cubelover play a game of Nim. The game uses $N$ piles of stones, and every pile holds at least one stone.

The two players take turns. On your turn you pick one pile that still has stones and remove at least one stone from it. The player who removes the last stone of all the piles wins.

koosaga moves first. Determine who wins when both players play optimally.

Input

The first line contains the number of piles $N$ ( $1 \le N \le 100$ ).

The second line contains the pile sizes $P_1, P_2, \dots, P_N$ separated by spaces ( $1 \le P_i \le 10^9$ ).

Output

Print the name of the winner on the first line: koosaga if koosaga wins, cubelover if cubelover wins.