Two players $A$ and $B$ are playing a game.They are given $N$ binary numbers as input. Each binary number is represented as a string of characters '0' or '1'. The string always ends at '1'.  In one move each player decides a bit position $p$ . Then he visits all the numbers and if their bit at that position is '1' then he changes it to '0'. It is mandatory to flip(change '1' to '0') bit of atleast one number in each move. The player who is unable to make a move loses. Player $A$ begins the game.

Input
First line contains a number $N$ as input. Next $N$ lines contain a binary string each.

Output
Print A if player A wins , B otherwise. In the next line print the move number of the last move of the winning player.

Constraints
$1 \le N \le 10^5$
$1 \le |S| \le 10^6$ where $|S|$ is sum of length of all bit strings.

Some important information - 
Suppose that the length of the string $S$ in input is $K$ then $S[0]$ is the $0^{th}$ bit , $S[1]$ is the first bit and so on $S[k - 1]$ is the $(k - 1)^{th}$ bit. All the other bit for that string are assumed as zeros. 

Note: Go through the sample explanation carefully