Alice and Bob are playing a game called "City Map". The game consists of N cities numbered from 0 to N-1 and connected only by unidirected roads. They are also given N strings each of length N. The i-th string (beginning with i=0) will contain a '1' (all quotes are for clarity only) in position j if there is a road that leads directly from i to j, and a '0' if there is no road that leads directly from i to j. Alice needs to find the cities from which every other city can be reached. Bob needs to find the cities that can be reached from every other city. The score of each player is the total number of cities he/she can find. The winner of the game is the one who scores more points. Assuming both Alice and Bob play optimally, your task is to find out the winner, or if the game ends in a draw (in case they have equal scores).
Input consists of several test cases, separated by blank lines
For each testcase, the first line contains N, the number of cities.
This is followed by N strings, each string in a separate line.
The last test case is followed by -1.
For each test case, the output consists of two lines.
The first line prints "Alice Wins" or "Bob Wins" or "Draw".
The second line contains the scores of Alice and Bob respectively separated by a space.
Each test case is followed by a new line.
- 2 <= N <= 50
- The i-th string will contain 0 in position i