Problem3389--Furlo and Rublo and Game

3389: Furlo and Rublo and Game

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Furlo and Rublo play a game. The table has n piles of coins lying on it, the i-th pile has ai coins. Furlo and Rublo move in turns, Furlo moves first. In one move you are allowed to:

  • choose some pile, let's denote the current number of coins in it as x;
  • choose some integer y (0≤y<x;x1/4≤y≤x1/2) and decrease the number of coins in this pile to y. In other words, after the described move the pile will have y coins left.

The player who can't make a move, loses.

Your task is to find out, who wins in the given game if both Furlo and Rublo play optimally well.

Input

The first line contains integer n (1≤n≤77777) − the number of piles. The next line contains n integers a1,a2,...,an (1≤ai≤777777777777) − the sizes of piles. The numbers are separated by single spaces.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

If both players play optimally well and Furlo wins, print "Furlo", otherwise print "Rublo". Print the answers without the quotes.

Examples
Input
1
1
Output
Rublo
Input
2
1 2
Output
Rublo
Input
10
1 2 3 4 5 6 7 8 9 10
Output
Furlo

Source/Category

 
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