In any permutation of 1, 2, 3, ..., 7, 8, how many permutations are there that make two adjacent numbers relatively prime?
在1，2，3，…，7，8的任意排列中，使得相邻两数互质的排列方式共有多少种．
<gadget id="calculator">4 * 3 * 2</gadget>
<output>24</output>

<gadget id="calculator">24 * 3 * 24</gadget>
<output>1_728</output>

<result>1_728</result>