A Senate committee has 5 Democrats and 5 Republicans.  In how many distinguishable ways can they sit around a circular table if all the members of each party all sit next to each other?  (If the table is rotated, it should be counted as the same seating.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A Senate committee has 5 Democrats and 5 Republicans.  In how many distinguishable ways can they sit around a circular table if all the members of each party all sit next to each other?  (If the table is rotated, it should be counted as the same seating.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
14,\!400
A Senate committee has 5 Democrats and 5 Republicans.  In how many distinguishable ways can they sit around a circular table if all the members of each party all sit next to each other?  (If the table is rotated, it should be counted as the same seating.)
train