A box contains eight balls, two of each color red, blue, green, and purple. Doug randomly selects two of the balls without replacement, records the colors of the two balls, and then returns the balls to the box. Then Becky also randomly selects two of the balls, records the colors, and returns the balls to the box. Finally, Travis repeats what Doug and Becky have done. The probability that the six colors recorded by Doug, Becky, and Travis include at least one of each of the colors red, blue, green, and purple is m/n , where m and n are relatively prime positive integers. Find m + n.