Matrix Game

Interview

Time limit0.5sMemory limit512 MB

Summary

Given an N by M matrix, it asks who wins a take-away game where a move subtracts 1 to K from the leftmost nonzero entry of some row.

Level: Medium7 of 10
Topics: Game theory, Greedy, Hash map, Matrix
Solved: No attempts yet

Problem

Koosaga and Cubelover are about to play a matrix game. The matrix game is played on an N×M matrix, with the two players taking turns, according to the following rules.

Choose a row that contains at least one nonzero number. In that row, choose the leftmost nonzero number. Let the chosen number be K, and decrease it. The number must be decreased by at least 1 and at most K.

The game ends when every number in the matrix becomes 0. The player who decreases a number last wins the game.

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

Input

The first line gives N and M. The following N lines give the integers in the matrix. Every number in the input is a natural number less than or equal to 1,000.

Output

If Koosaga wins the game, print "koosaga"; if Cubelover wins, print "cubelover".

Examples5

Example 1
Input
```
2 2
1 1
1 1
```
Expected output
```
cubelover
```
Example 2
Input
```
1 3
2 1 1
```
Expected output
```
koosaga
```
Example 3
Input
```
2 2
3 2
3 2
```
Expected output
```
cubelover
```
Example 4
Input
```
3 4
1 2 3 4
2 3 4 5
3 4 5 6
```
Expected output
```
koosaga
```

Example 5

Input

Expected output

cubelover