## MOG Round #35## Ended |

Brian and Fito are playing a game with candies. Initially, there are $N$ heaps where the $i$-th of them has $a_i$ candies. In his turn, a player can only take a positive number of candies from one of the heaps. Brian plays first and they alternate moves.

If the $\text{XOR}$ sum, $a_1\, \text{XOR}\, a_2\, \text{XOR}\, ... \text{XOR}\, a_N$, of the numbers of remaining candies of these heaps, becomes $0$ as a result of a player's move, the player loses.

Given the initial configuration of the heaps, your task is to write a program that determines who will win the game. This can help Fito to decide an initial configuration that allows him to win.

The input consists of a single test case. The first line contains an integer $N$ ($1 \leq N \leq 10^5$) which is the number of heaps. Each of the following $N$ lines contains an integer $a_i$ ($1 \leq a_i \leq 10^9$) that represents the number of candies in the $i$-th heap.

Print one line with "Brian" if he wins (assuming he plays optimally), or "Fito" if he has a chance to win (no matter how Brian plays).

Input

1
1

Output

Fito

Input

2
1
1

Output

Brian

Input

3
1
2
3

Output

Brian