Astrid has 12 blocks, 2 of each are red (R), blue (B), yellow (Y), green (G), orange (O), and purple (P). Call an arrangement of blocks even if there is an even number of blocks between each pair of blocks of the same color. Astrid arranges her blocks in a row in random order. The probability that her arrangement is even is m/n, where m and n are relatively prime positive integers. Find m+n.
