I. Red Envelopes
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

In preparing for the festivities, you have laid out $$$n$$$ envelopes, each containing some number of coins. You go to sleep, but two sneaky children named Ai and Bo are trying to steal some of the coins! Of course, there is some method to their madness, so they decide to play the following game.

Ai and Bo take turns, with Ai going first. On each turn, the current player must pick some non-empty subset of envelopes that currently have the same non-zero number of coins. Then, they will take 1 coin from each of the envelopes they selected. If there are no more coins in any envelope, then the game ends.

Interestingly, they don't care about the total number of coins that they each collect, but just whoever makes the final move wins. Given the number of coins in each envelope and that Ai and Bo play optimally, can you determine who wins?

Input

The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of envelopes.

The next line contains $$$n$$$ space-separated integers $$$a_1, a_2, ..., a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the number of coins in the $$$i$$$th envelope.

Output

Output "Ai" (without the quotes) if Ai will win the game assuming perfect strategy, and "Bo" otherwise.

Examples
Input
2
1 1
Output
Ai
Input
1
2
Output
Bo
Input
5
1 2 3 4 5
Output
Ai
Input
4
1 2 2 3
Output
Bo
Note

In the first test case, Ai can select both envelopes containing 1 coin and win.

In the second test case, there is only one envelope with 2 coins, so Ai can only take a coin from that envelope, followed by Bo taking a coin from the envelope and winning.