Five people each take a bucket and wait in front of the tap to fetch water. The time it takes them to fetch water is 1 minute, 2 minutes, 3 minutes, 4 minutes, and 5 minutes. If there is only one tap to properly arrange their order of fetching water, It can minimize the sum of everyone's queuing and fetching time, so how many minutes is this minimum?
5个人各拿一个水桶在自来水龙头前等候打水，他们打水所需要的时间分别是1分钟、2分钟、3分钟、4分钟和5分钟，如果只有一个水龙头适当安排他们的打水顺序，就能够使每个人排队和打水时间的总和最小，那么这个最小值是多少分钟？
<gadget id="calculator">5 * 1</gadget>
<output>5</output>

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">5 + 8 + 9 + 8 + 5</gadget>
<output>35</output>

<result>35</result>