Root Game

Interview

Time limit1sMemory limit512 MB

Summary

For each N, decide who wins the subtraction game where a move subtracts any perfect square from a running total and taking the last square wins.

Level: Medium5 of 10
Topics: Game theory, Dynamic programming, Math, Brute force
Solved: No attempts yet

Problem

Koosaga and Cubelover are about to play the root game. The root game uses a single integer, and initially this integer is N.

The two players take turns, and Koosaga moves first. On each turn, a player chooses a perfect square x greater than or equal to 1 and subtracts x from N. The integer may not become negative, and the player who makes it 0 wins the game.

Write a program that determines who wins when both players play optimally.

Input

The first line gives the number of test cases T (1 ≤ T ≤ 105). The next T lines give the test cases, one per line, each containing N (1 ≤ N ≤ 106).

Output

For each test case, print the winner. Print "koosaga" if Koosaga wins, and "cubelover" if Cubelover wins.

Examples1

Example 1
Input
```
3
1
2
3
```
Expected output
```
koosaga
cubelover
koosaga
```