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.IOException;
import java.util.Scanner;
class Main{
	public static void main(String[] args)throws NumberFormatException, IOException{
		Scanner scan = new Scanner(System.in);
		int decTimes = scan.nextInt();
		int diceNum[][] = new int[decTimes][6];
		boolean sameDice = false;
		diceClass dice = new diceClass();

		for (int i=0; i<decTimes; i++){
			for (int ii=0; ii<6; ii++){
				diceNum[i][ii] = scan.nextInt();
			}
		}
		int[] diceA = new int[6];
		int[] diceB = new int[6];

		//??????????????°???????????£??\??????
		for(int iA=0; iA<decTimes; iA++){
			diceA[0] = diceNum[iA][0];
			diceA[1] = diceNum[iA][1];
			diceA[2] = diceNum[iA][2];
			diceA[3] = diceNum[iA][3];
			diceA[4] = diceNum[iA][4];
			diceA[5] = diceNum[iA][5];
			for(int iB=0; iB<decTimes; iB++){
				if(iA != iB){
					diceB[0] = diceNum[iB][0];
					diceB[1] = diceNum[iB][1];
					diceB[2] = diceNum[iB][2];
					diceB[3] = diceNum[iB][3];
					diceB[4] = diceNum[iB][4];
					diceB[5] = diceNum[iB][5];
				}
				//??????????????¢?????????????????????
				for(int rotate1=0; rotate1<4; rotate1++){
					for(int rotate2=0; rotate2<4; rotate2++){
						for(int rotate3=0; rotate3<4; rotate3++){
							sameDice = dice.compare(diceA, diceB);
							if(sameDice == true){
								break;
							}
							diceB = dice.move(rotate1);
							sameDice = dice.compare(diceA, diceB);
							if(sameDice == true){
								break;
							}
							diceB = dice.move(rotate2);
							sameDice = dice.compare(diceA, diceB);
							if(sameDice == true){
								break;
							}
							diceB = dice.move(rotate3);
							sameDice = dice.compare(diceA, diceB);
							if(sameDice == true){
								break;
							}
						}
						if(sameDice == true){
							break;
						}
					}
					if(sameDice == true){
						break;
					}
				}
				if(sameDice == true){
					break;
				}
			}
			if(sameDice == true){
				break;
			}
		}

		if(sameDice == true){
			System.out.println("No");
		}
		else{
			System.out.println("Yes");
		}
	}
}

class diceClass{	
	int pos[] = new int[6];
	int up0[] = {1,2,4,3};
	int up1[] = {0,3,5,2};
	int up2[] = {0,1,5,4};
	int up3[] = {0,4,5,1};
	int up4[] = {0,2,5,3};
	int up5[] = {1,3,4,2};
	public diceClass(){

	}

	public int[] move(int direction){		//?????????????????¢?????????????????°????????????
		int[] temp = (int[])pos.clone();
		if(direction == 0){
			pos[0] = temp[1];
			pos[1] = temp[5];
			pos[2] = temp[2];
			pos[3] = temp[3];
			pos[4] = temp[0];
			pos[5] = temp[4];
		}
		else if(direction == 1){
			pos[0] = temp[3];
			pos[1] = temp[1];
			pos[2] = temp[0];
			pos[3] = temp[5];
			pos[4] = temp[4];
			pos[5] = temp[2];
		}
		else if(direction == 2){
			pos[0] = temp[2];
			pos[1] = temp[1];
			pos[2] = temp[5];
			pos[3] = temp[0];
			pos[4] = temp[4];
			pos[5] = temp[3];
		}
		else if(direction == 3){
			pos[0] = temp[4];
			pos[1] = temp[0];
			pos[2] = temp[2];
			pos[3] = temp[3];
			pos[4] = temp[5];
			pos[5] = temp[1];
		}
		return pos;
	}

	public boolean compare(int[] n1,int[] n2){		//???????????????????????§??????????????????
		if(n1[0] == n2[0] && n1[1] == n2[1] && n1[2] == n2[2]
				&& n1[3] == n2[3] && n1[4] == n2[4] && n1[5] == n2[5]){
			return true;
		}
		else{
			return false;
		}
	}
}