You are given a sequence of $N$ positive integers $A = (A_1, A_2, \dots ,A_N)$, where each element is at least $2$. Anna and Bruno play a game using these integers. They take turns, with Anna going first, performing the following operation.

• Choose an integer $i \ (1 \leq i \leq N)$ freely. Then, freely choose a positive divisor $x$ of $A_i$ that is not $A_i$ itself, and replace $A_i$ with $x$.

The player who cannot perform the operation loses, and the other player wins. Determine who wins assuming both players play optimally for victory.

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Print Anna if Anna wins the game, and Bruno if Bruno wins.

• $1 \leq N \leq 10^5$
• $2 \leq A_i \leq 10^5$
• All input values are integers.

For example, the game might proceed as follows. Note that this example may not necessarily represent optimal play by both players:

• Anna changes $A_3$ to $2$.
• Bruno changes $A_1$ to $1$.
• Anna changes $A_2$ to $1$.
• Bruno changes $A_3$ to $1$.
• Anna cannot operate on her turn, so Bruno wins.

Actually, for this sample, Anna always wins if she plays optimally.