3618: Furlo and Rublo and Game
Description
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.
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.
If both players play optimally well and Furlo wins, print "Furlo", otherwise print "Rublo". Print the answers without the quotes.
1
1
Rublo
2
1 2
Rublo
10
1 2 3 4 5 6 7 8 9 10
Furlo