Thammasat Science Sports Day $($CstuSportsFest$)$

Semester $2,$ academic year $2020,$ Thammasat University

By Khanajarn Wicha K$.$P$\mathrm{.}300$

In the year $3000,$ the Department of Computer Science, Thammasat University, will organize a sports day. For each color, the color supervisor must select $2$ athletes of each color to compete in the programming sport. The selection will be considered. "Incompatibility" of the two athletes This mismatch is defined by the similarity of student characteristics. The characteristics of each student are measured by giving. Students answer a number of questionnaires$/$items$.$ Each question will be given a score of $1,2,3,4,$ or $5.$

For example, if a faculty member determines to use a questionnaire with $2$ questions as follows:

$(1)$ Do students like to eat Japanese food?

$[1]$

$[2]$

$[3]$

$[4]$

$[5]$

$(2)$ Do students like to exercise or not?

$[1]$

$[2]$

$[3]$

$[4]$

$[5]$

And there were $3$ students who answered the questionnaire and the details are as follows.

Student $1$ rated item $1$ as $3$ and rated item $2$ as $1.$

Student $2$ rated item $1$ as $1$ and rated item $2$ as $5.$

Student $3$ rated Item $1$ as $4$ and rated Item $2$ as $4.$

From the query we can use a vector $(1$D array of size N$).$

vi $=$ v$1,$v$2,$v$3,.....,$vn

To represent the questionnaire responses of the i$-$th student, the member in the vector vi is the score that the student answered in questionnaire number $1.$ As in the example above, we get that

Student $1$ is represented by v$1=[3,1]$

Student $2$ is represented by v$2=[2,5],$

Student number $3$ is represented by v$3=[4,4],$

From this feature vector, we can find the $$mismatch$$ of two students v$1,$ v$2$ with the power of Euclidean distance of $2$ as follows: Dv$1,$v$2=$ zigma$($v$1-$v$2),$ where the higher the values of Dv$1,$v$2,$ A high value means that the two students do not get along well. While the higher the value of Dv$1,$v$2,$ the smaller the value means These two students are more likely to get along with each other.

Substituting the values, we can find Dv$1,$ v$2=(31)^2+(15)^2=4+16=20$

and Dv$1,$v$3,=(34)^2+(14)^2=1+9=10$

When Dv$1,$v$2>$ Dv$1,$v$3,$ it means that Student $1$ is more compatible with Student $3$ than Student $2$ because of their scores. The incompatibility scores of students $1$ and $3$ were less than the incompatibility scores of students $1$ and $2.$

And when we calculated Dv$2,$v$3=(24)^2+(54)^2=4+1=5,$ it was found that students $2$ and $3$ had the lowest incompatibility scores. That is$,$ students $2$ and $3$ are most compatible with each other. Students $2$ and $3$ were therefore selected to compete.

sports day

Problems

Have students write a program to help teachers of each color select $2$ students by calculating the lowest incompatibility score. So that the two students who will be selected will be as compatible as possible. From a total of M students to participate in the writing competition. The program for the Thammasat Science and Technology Sports Festival $2000$ follows the criteria above. $($Assume that all students answer the questionnaire. has been completed$)$ with details of the input and output of the program as follows:

Observations$/$Hints: If you want the program to be able to calculate values correctly. The program must check every possible pair of students. For example, if there are a total of $3$ students in a color, the program must check all $3$ pairs of students $(1,2),(1,3),$ and $(2,3)$ similar to what was calculated. Calculating from the example above, in the case where there are $4$ students, the program must check all $6$ pairs of students $(1,2)(1,3)(1,4)(2,3)(2,4)(3,4)$

input data

The input data has M $+1$ lines, where M is the total number of students participating in the selection.

Line $1,$ integer $2,$ number M and N$,$ where N is the number of questionnaire items to measure student incompatibility, where $2<=$ M $<=10$ and $1<=$ N $<=15.$

Lines $2$ through M $+1$ each take an integer N$.$ The numbers tell details about responses to queries $1$ through N$,$ with each value being an integer in the range $1$ through $5.$

Note: All input data must always have the correct value according to the format, scope, and set of possible values. Students do not need to validate the input data.

Export data

The output data has only one line: the incompatibility score $($D$)$ is always a positive integer. with the least value from students Every couple that is selected $($In the case where there is more than $1$ pair with the same incompatibility score, answer with only $1$ incompatibility score.$)$

Example $1$

input data

$22$

$45$

$45$

Export data

$0$

Example $2$

input data

$53$

$421$

$122$

$133$

$123$

$456$

Export data

$1$

Example $3$

input data

$54$

$1111$

$5555$

$2345$

$3451$

$5115$

Export data

$14$