Our genetic material, DNA, is formed from a 4 letter "alphabet" of bases: A, T, G, C (adenine, thymine, guanine, and cytosine). The order in which the letters are arranged is important, but because a molecule can move, there is no difference between a sequence and the same sequence reversed. For example, the sequence (A, A, T, A, G, A, T) is the same as the sequence (T, A, G, A, T, A, A). (In reality, DNA molecules have identifiable ends, but ignore that in this problem.)

How many distinct DNA sequences of 11 bases are there?