# Problem 380: Amazing Mazes!
An m×n maze is an m×n rectangular grid with walls placed between grid
cells such that there is exactly one path from the top-left square to
any other square. The following are examples of a 9×12 maze and a 15×20
maze: Let C(m,n) be the number of distinct m×n mazes. Mazes which can be
formed by rotation and reflection from another maze are considered
distinct. It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415,
and C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant
digits). Find C(100,500) and write your answer in scientific notation
rounded to 5 significant digits. When giving your answer, use a
lowercase e to separate mantissa and exponent. E.g. if the answer is
1234567891011 then the answer format would be 1.2346e12.