Quarry Game

Time limit2sMemory limit512 MB

Summary

Each of N piles is a run of M consecutive pile sizes starting at X; a move takes at least one stone from one pile. Decide the winner under optimal play.

Level: Hard9 of 10
Topics: Game theory, Math, Combinatorics, Number theory
Solved: No attempts yet

Problem

Koosaga and Cubelover own $N$ quarries. Today they want to play a game with the quarries.

Each quarry holds some dump trucks. The number of dump trucks parked in the $i$ -th quarry is $M_i$ . Each dump truck carries stones: the first truck carries $X_i$ stones, the second carries $X_i+1$ stones, the third carries $X_i+2$ stones, ..., and the $M_i$ -th truck carries $X_i+M_i-1$ stones.

The two players take turns, and Koosaga moves first. On your turn you must choose one dump truck and remove stones from it. The number of stones removed must be at least 1. The player who cannot remove any more stones loses.

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

Input

The first line gives the number of quarries $N$ ( $1 \le N \le 100,000$ ). The next $N$ lines give the quarry information. Each quarry is described by two integers $X_i, M_i$ ( $1 \le X_i, M_i \le 10^{16}$ ).

Output

Print "koosaga" if Koosaga wins, and "cubelover" if Cubelover wins.

Examples2

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