A tribute to Cody's five-year anniversary should also celebrate the people behind Cody, and in this particular case, our illustrious Quizmaster, Ned Gulley.

The N-Queens problem (N stands for Ned, of course) is a well known computing challenge. If you are unfamiliar with this problem, refer to Problem 113, incidentally written by... You guessed it.

This problem is the real deal. Given a positive integer, n, representing the number of queens and the size of the board, return the number of possible solutions, s, and a list of the solutions, q.

q shall be an array with s rows and n columns, such that each row represents one solution. The column indeces of q shall represent the column indeces of the positions of the queens in the respective solution, while the values of the array elements shall represent the row indeces of the positions of the queens in the respective solution. q does not have to be sorted.

Note: All symmetries/rotations count as individual solutions.

Example:

 Input: n = 4

 Output: s = 2, q = [2 4 1 3;3 1 4 2]