2016 AIME II Problem 13

Beatrix is going to place six rooks on a 6 \times 6 chessboard where both the rows and columns are labeled 1 to 6 ; the rooks are placed so that no two rooks are in the same row or the same column. The value of a square is the sum of its row number and column number. The score of an arrangement of rooks is the least value of any occupied square. The average score over all valid configurations is \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.