Each of the four people carries a bucket to the faucet to collect water. The time required for the faucet to fill the buckets of the four people is 5 minutes, 4 minutes, 3 minutes, and 6 minutes respectively. Now only one faucet is available. How to arrange the connection of the four people? Water order, can make their total waiting time the shortest? What is the minimum time?
四个人各提一只水桶到水龙头接水，水龙头灌满4个人的水桶所需时间分别是5分钟、4分钟、3分钟、6分钟，现在只有一个水龙头可用，问怎样安排这4个人的接水次序，可以使他们总的等候时间最短？这个最短时间是多少？
<gadget id="calculator">1 * 6</gadget>
<output>6</output>

<gadget id="calculator">2 * 5</gadget>
<output>10</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">4 * 3</gadget>
<output>12</output>

<gadget id="calculator">6 + 10 + 12 + 12</gadget>
<output>40</output>

<result>40</result>