Problem:
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Dice IV

Write a program which reads $n$ dices constructed in the same way as Dice I, and determines whether they are all different. For the determination, use the same way as Dice III.

Input

In the first line, the number of dices $n$ is given. In the following $n$ lines, six integers assigned to the dice faces are given respectively in the same way as Dice III.

Output

Print "Yes" if given dices are all different, otherwise "No" in a line.

Constraints

$2 \leq n \leq 100$

$0 \leq $ the integer assigned to a face $ \leq 100$

Sample Input 1

3
1 2 3 4 5 6
6 2 4 3 5 1
6 5 4 3 2 1

Sample Output 1

No

Sample Input 2

3
1 2 3 4 5 6
6 5 4 3 2 1
5 4 3 2 1 6

Sample Output 2

Yes

Solution in JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
 
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        boolean flag = false;
        int n = Integer.parseInt(br.readLine());
        String str[] = new String[n];
        for(int i=0;i<n;i++){
            str[i] = br.readLine();
        }
        label:for(int i=0;i<n-1;i++){
            for(int j=i+1;j<n;j++){
                flag = Dice.checkSame(str[i], str[j]);
                if(flag == true) break label;
            }
        }
        if(flag){
            System.out.println("No");
        }else{
            System.out.println("Yes");
        }
    }
}
 
class Dice{
    private String str[];//0=top,1=front,2=right,3=left,4=back,5=bottom
    private String tmp;
     
    Dice(String str) {
        this.str = new String[6];
        this.str = str.split(" ");
    }
     
    public String getStr(int n){
        return this.str[n];
    }
     
    void moveW(){
        tmp = this.str[0];
        this.str[0] = this.str[2];
        this.str[2] = this.str[5];
        this.str[5] = this.str[3];
        this.str[3] = tmp;
    }
     
    void moveE(){
        tmp = this.str[0];
        this.str[0] = this.str[3];
        this.str[3] = this.str[5];
        this.str[5] = this.str[2];
        this.str[2] = tmp;
    }
     
    void moveS(){
        tmp = this.str[0];
        this.str[0] = this.str[4];
        this.str[4] = this.str[5];
        this.str[5] = this.str[1];
        this.str[1] = tmp;
    }
     
    void moveN(){
        tmp = this.str[0];
        this.str[0] = this.str[1];
        this.str[1] = this.str[5];
        this.str[5] = this.str[4];
        this.str[4] = tmp;
    }
     
    static boolean checkSame(String dice1Str, String dice2Str){
        Dice dice1 = new Dice(dice1Str);
        Dice dice2 = new Dice(dice2Str);
        int i,j,count=0;
        boolean check = false;
        String str = "";
        for(i=0;i<6;i++){
            if(dice1.getStr(0).equals(dice2.getStr(i))){
                count++;
                str += String.valueOf(i);
            }
        }
        label:for(i=0;i<count;i++){
            dice2 = new Dice(dice2Str);
            switch(Integer.parseInt(str.substring(i,i+1))){
                case 1:
                    dice2.moveN();
                    break;
                case 2:
                    dice2.moveW();
                    break;
                case 3:
                    dice2.moveE();
                    break;
                case 4:
                    dice2.moveS();
                    break;
                case 5:
                    dice2.moveN();
                    dice2.moveN();
                    break;
                case 0:
                default:
                    break;
            }
            int count2 = 0;
            String str2 = "";
            for(j=1;j<5;j++){
                if(dice1.getStr(1).equals(dice2.getStr(j))){
                    count2++;
                    str2 += String.valueOf(j);
                }
            }
            if(count2 != 0){
                for(int k=0;k<count2;k++){
                    switch(Integer.parseInt(str2.substring(k,k+1))){
                        case 1:
                            if(dice1.getStr(2).equals(dice2.getStr(2)) && 
                               dice1.getStr(3).equals(dice2.getStr(3)) && 
                               dice1.getStr(4).equals(dice2.getStr(4)) &&     
                               dice1.getStr(5).equals(dice2.getStr(5))){
                                check = true;
                                break label;
                            }
                            break;
                        case 2:
                            if(dice1.getStr(2).equals(dice2.getStr(4)) && 
                               dice1.getStr(3).equals(dice2.getStr(1)) && 
                               dice1.getStr(4).equals(dice2.getStr(3)) &&     
                               dice1.getStr(5).equals(dice2.getStr(5))){
                                check = true;
                                break label;
                            }
                            break;
                        case 3:
                            if(dice1.getStr(2).equals(dice2.getStr(1)) && 
                               dice1.getStr(3).equals(dice2.getStr(4)) && 
                               dice1.getStr(4).equals(dice2.getStr(2)) &&     
                               dice1.getStr(5).equals(dice2.getStr(5))){
                                check = true;
                                break label;
                            }
                            break;
                        case 4:
                            if(dice1.getStr(2).equals(dice2.getStr(3)) && 
                               dice1.getStr(3).equals(dice2.getStr(2)) && 
                               dice1.getStr(4).equals(dice2.getStr(1)) &&     
                               dice1.getStr(5).equals(dice2.getStr(5))){
                                check = true;
                                break label;
                            }
                            break;
                        default:
                            break;
                    }
                }
            }
        }
        return check;
    }
}