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.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner std = new Scanner(System.in);
        int n = Integer.parseInt(std.next());

        int defaultpip[][] = new int[n][6];
        ArrayList<Dice> dc = new ArrayList<Dice>();

        for(int j=0; j<n; j++){
            for(int i=0; i<6; i++){
                defaultpip[j][i] = Integer.parseInt(std.next());
            }
            dc.add(new Dice(defaultpip[j]));
        }
        Dice dcarray[] = (Dice[])dc.toArray(new Dice[n]);
        dc.clear();
        //??¬???????????¬???
        String query[] = {"S", "W", "N", "E"};

        boolean diff = false;
        ALLLOOP:
        for(int k=0; k<n-1; k++){
        for(int j=k+1; j<n; j++){
            diff = false;
            for(int i = 0; i<100; i++){
                if(dcarray[j].issame(dcarray[k])){
                    break ALLLOOP;
                }else{
                    dcarray[j]=dcarray[j].newnowpips(query[(int)(Math.random()*4)]);
                }
            }
            diff = true;
        }
        }
        if(diff){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
    }
}

class Dice {
	int pips[];
	int nowpip;
	int spip;
	int epip;
	int wpip;
	int npip;
	int rpip;

	public Dice(int pip[]){
		this(pip, 0, 1, 2, 3, 4, 5);
	}

	public Dice(int pip[], int now, int s, int e, int w, int n, int r){
		pips = pip;
		nowpip = now;
		spip = s;
		epip = e;
		wpip = w;
		npip = n;
		rpip = r;
	}

	public Dice newnowpips(String query){
		if(query.equals("N")){
			return new Dice(pips,spip,rpip,epip,wpip,nowpip,npip);
		}else if(query.equals("E")){
			return new Dice(pips,wpip,spip,nowpip,rpip,npip,epip);
		}else if(query.equals("S")){
			return new Dice(pips,npip,nowpip,epip,wpip,rpip,spip);
		}else if(query.equals("W")){
			return new Dice(pips,epip,spip,rpip,nowpip,npip,wpip);
		}else {	//clockwise
			return new Dice(pips,nowpip,epip,npip,wpip,spip,rpip);
		}
	}

	public String showdice(){
		return pips[nowpip] +" "+ pips[spip] +" "+ pips[epip] +" "+ pips[wpip] +" "+ pips[npip] +" "+ pips[rpip];
	}

	public boolean issame(Dice d2){
		return pips[nowpip] == d2.pips[d2.nowpip] && pips[npip] == d2.pips[d2.npip] && pips[epip] == d2.pips[d2.epip] &&
				pips[spip] == d2.pips[d2.spip] && pips[wpip] == d2.pips[d2.wpip] && pips[rpip] == d2.pips[d2.rpip];
	}
}