This is an interactive problem.
Alice and Bob are playing a game. There is a row consisting of $$$n$$$ piles of stones, where the $$$j$$$-th pile contains $$$a_j$$$ stones. On each player's turn, with Alice going first, they remove one stone from any nonempty pile, and the first player who is unable to make a move loses.
However, they have gotten bored with this game, so, inspired by ultimate tic-tac-toe, they have developed a new version, in which there are $$$n$$$ initially identical rows of stones. For example, if $$$a = [3, 0, 1, 4]$$$, the game would initially look like this:
On her first turn, Alice may remove a stone from a pile in any row she chooses, and after that, if the previous player removed from the $$$j$$$-th pile in a row, the current player must choose a pile in the $$$j$$$-th row.
Alice and Bob have both asked you to help them win the game. You must pick which player to assist, and help them win the game.
Each test consists of multiple test cases.
The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of rows, as well as the number of piles in each row.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \cdots a_n$$$ ($$$0 \le a_j \le 100$$$), where $$$a_j$$$ is the number of stones in the $$$j$$$-th pile of each of the rows.
It is guaranteed that the sum of $$$n$$$ across all test cases is at most $$$100$$$, and the sum of $$$\sum_{j=1}^n a_j$$$ across all test cases is at most $$$100$$$.
After reading in the $$$a_j$$$ values for each test case, print a single line containing either the word Alice or Bob — the name of the player you wish to assist.
After you print this line, the game will begin, with you playing as your chosen player and the judge playing as your opponent.
On each player's turn, they must print two integers $$$i$$$ and $$$j$$$ ($$$1 \le i, j \le n$$$) — the row number and pile number from which they will remove a stone. This pile must not be empty, and if it is not the first turn, the $$$i$$$ value printed must match the $$$j$$$ value printed by the previous player.
If the judge has no legal moves on its turn, it will instead print 0 0, indicating that you have won the game, and can proceed to the next test case, or terminate your program if this was the last test case. You must win all test cases to receive the Accepted verdict.
If you remove from an empty pile, or an invalid row, the judge will respond with -1 -1. If you receive this output from the judge, you must terminate your program in order to receive the Wrong Answer verdict. Otherwise, you can receive an arbitrary verdict because your solution is reading from a closed stream.
After printing your chosen player, and after making each of your moves, do not forget to flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
- fflush(stdout) or cout.flush() in C++;
- System.out.flush() in Java;
- flush(output) in Pascal;
- stdout.flush() in Python;
- see the documentation for other languages.
2 2 1 2 2 2 2 1 0 0 4 0 0 0 0 0 0
Alice 1 2 2 2 1 2 Bob
Here is the sequence of moves in the first test case. Alice's moves are shown in red, and Bob's are shown in blue. In the final step, Bob must remove a stone from a pile in the second row, however these are all empty, so he loses.
In the second test case, all $$$a_j$$$ are zero initially, so Alice is unable to make her first move, and Bob wins.
