Problem Statement

Alice and Bob play a game.

Initially there are $N$ piles, and the $i$-th pile has $A_i$ stones on it.

Starting with Alice, the $2$ players alternately and repeatedly choose one of the following operations.

1. Choose $1$ pile that has $1$ or more stones remaining. If the chosen pile has $X$ stones, remove any number of stones between $1$ and $X$, inclusive, from that pile. If all the stones are removed, that is, if $X$ stones are removed, the player gets $1$ coin as a bonus.
2. Discard $1$ coin that the player has.

The player who first becomes unable to perform an operation loses.

Initially, neither Alice nor Bob has any coins. Determine who wins when both Alice and Bob act optimally in order to win.

For each input file, answer $T$ test cases.

Constraints

Input

The input is given from standard input in the following format.

$T$
$\mathrm{case}_1$
$\vdots$
$\mathrm{case}_T$

Each test case is given in the following format.

$N$
$A_1$ $A_2$ $\dots$ $A_N$

Output

Output $T$ lines. On the $i\ (1\le i \le T)$-th line, output Alice if the winner of the $i$-th test case is Alice, and Bob if it is Bob.

Sample

2
1
3
2
1 1

Alice
Bob