Arrange the 14 numbers 26, 28, 30, 32, ..., 46, 48, 50, 52 in a row so that the sum of 3 adjacent numbers in each group is a multiple of 3. How many ways are there in total?
将26、28、30、32、…、46、48、50、52这14个数排成一行，使得每组相邻3个数的和都是3的倍数，共有多少种排法？
<gadget id="calculator">4 * 3 * 2 * 1</gadget>
<output>24</output>

<gadget id="calculator">1_440 * 24</gadget>
<output>34_560</output>

<gadget id="calculator">34_560 * 2</gadget>
<output>69_120</output>

<result>69_120</result>