Teacher Li, Teacher Gao, and Teacher Cai went to the General Affairs Office to pay the book fees at the same time. Teacher Li needs 7 minutes, Teacher Gao needs 5 minutes, and Teacher Cai needs 4 minutes. How to arrange their payment order so that the sum of the payment and waiting time of these three people is the least? How many minutes at least?
李老师、高老师、蔡老师三人同时去总务处交书费．李老师需要7分钟，高老师需要5分钟，蔡老师需要4分钟．怎样安排他们的交费顺序，才能使这三人交费及等候的时间总和最少？最少需要几分钟？
<gadget id="calculator">4 + 5</gadget>
<output>9</output>

<gadget id="calculator">4 + 5 + 7</gadget>
<output>16</output>

<gadget id="calculator">4 + 9 + 16</gadget>
<output>29</output>

<result>29</result>