Four people A, B, C, and D cross a bridge at night, and the bridge can accommodate at most two people at a time. A flashlight is needed to cross the bridge, but the four people only have one flashlight. The time required for A, B, C, and D to cross the bridge alone is 1 minute, 2 minutes, 5 minutes, and 10 minutes, respectively. I would like to ask: How to arrange the order of crossing the bridge so that the total time for four people to cross the bridge is the shortest? How many minutes is this minimum time? (It is not allowed to throw the flashlight back after crossing the bridge, only people can carry it back)
甲、乙、丙、丁四个人在晚上过一座桥，桥每次最多容纳两个人一起通过．过桥需要手电筒，而四人只有1支手电筒，甲、乙、丙、丁单独过桥需要的时间分别为1分钟、2分钟、5分钟、10分钟．请问：怎样安排过桥顺序，才能使四个人过桥的总时间最短？这个最短时间是多少分钟？(不允许过桥后将电筒扔回，只能让人携带回来)
<gadget id="calculator">2 + 1 + 10 + 2 + 2</gadget>
<output>17</output>

<result>17</result>