On the $ xy $-plane, the origin is labeled with an $ M $. The points $ (1,0) $, $ (-1,0) $, $ (0,1) $, and $ (0,-1) $ are labeled with $ A $'s. The points $ (2,0) $, $ (1,1) $, $ (0,2) $, $ (-1, 1) $, $ (-2, 0) $, $ (-1, -1) $, $ (0, -2) $, and $ (1, -1) $ are labeled with $ T $'s. The points $ (3,0) $, $ (2,1) $, $ (1,2) $, $ (0, 3) $, $ (-1, 2) $, $ (-2, 1) $, $ (-3, 0) $, $ (-2,-1) $, $ (-1,-2) $, $ (0, -3) $, $ (1, -2) $, and $ (2, -1) $ are labeled with $ H $'s. If you are only allowed to move up, down, left, and right, starting from the origin, how many distinct paths can be followed to spell the word MATH?