According to the teaching plan, a school arranges students in all classes to have a physical fitness test to understand the students' physical fitness. The test includes five items: height and weight, standing long jump, vital capacity, grip strength and step test, all of which are automatically measured, recorded and saved by electronic instruments. The school introduced 3 height and weight measuring instruments, standing long jump and vital capacity measuring instrument 1 set, and 2 grip strength and step test measuring instruments.

Height and weight, standing long jump, vital capacity and grip strength, the average test time of each instrument for each student (including student conversion) is 10 second, 20 second, 20 second, 15 second respectively, and it takes 3 minutes and 30 seconds for each instrument to test 5 students.

Each student needs to input personal information, that is, student number, before testing each project, which takes an average of 5 seconds. After each student is tested, the student number of the instrument will automatically move back by one, so if the student number before and after the test is connected, the input time can be saved and the student number of the same class can be connected.

The school arranges the examination time every day at 8: 00- 12: 10 and 13: 30- 16: 45. The five tests were conducted in a small place with a maximum capacity of 150 people, and the test items were not in a fixed order. See the attached table for the number of classes participating in the physical fitness test.

The school requires all students in the same class to complete all exams in the same time period, and try to save students' waiting time when the number of time periods required for the whole exam is the least.

Please use mathematical symbols and language to express the examination schedule of each class, give the algorithm of this math problem, and try to show the examination schedule scheme to the faculty and students in a clear and intuitive form, explaining how the scheme meets the above requirements and conditions of the school.

Finally, please make suggestions on the following aspects of physical fitness test in schools in the future, and explain the reasons: for example, the number of imported measuring instruments; Personnel capacity of the test site; Whether students in a class need to be divided into several groups for testing.

List of students in each class participating in physical fitness test

Class number1234567891012131415.

Number 4145 44 44 26 44 42 20 38 37 25 45 45 45 45 45

Class number16171819 202122 23 24 25 26 27 28 29 30

Number 44 20 30 39 35 38 38 28 25 30 36 20 24 32 33

Class number 3132 33 34 35 36 37 38 39 40 4142 43 44 45

Number 4133 5139 20 44 37 38 39 42 40 37 50 50

Class number 46 47 48 49 50 5 1 52 53 54 55 56

No.42 43 465 438+0 42 45 4219 39 751717