Each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. For each square, either color is equally likely to be used. The probability of obtaining a grid that does not have a 2-by-2 red square is \(\frac {m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).
(第十九届AIME2 2001 第9题)