Xiaodong, Xiaofang, Xiaogang, and Xiaoling went to fetch water with 4, 3, 2, and 1 buckets respectively. There is only one faucet, and it takes 1 minute to fill a bucket of water. After reasonably arranging the order of the four of them in line, what is the minimum sum of the waiting time for them to fetch water?
小冬、小芳、小刚、小玲四人分别拿着4个、3个、2个、1个水桶去打水．水龙头只有一个，装满一桶水要1分钟．合理安排他们四人排队顺序后，他们打水的等待时间总和最少是多少分钟．
<gadget id="calculator">1 * 4</gadget>
<output>4</output>

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">4 * 1</gadget>
<output>4</output>

<gadget id="calculator">4 + 6 + 6 + 4</gadget>
<output>20</output>

<result>20</result>