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 {
        // TODO 自動生成されたメソッド・スタ
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        Dice4[] dice = new Dice4[n];

        for (int i = 0; i < n; i++) {
            String[] inputs = br.readLine().split(" ");
            int[] input = new int[6];
            for (int j = 0; j < 6; j++) {
                input[j] = Integer.parseInt(inputs[j]);
            }
            dice[i] = new Dice4(input);
        }
        boolean result = false;
        outer: for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                if(dice[i].superEquals(dice[j])){
                    result = true;
                    break outer;
                }
            }
        }
        if(result){
            System.out.println("No");
        }else{
            System.out.println("Yes");
        }

    }

}

class Dice4 {
    int TOP, BOTTOM, LEFT, RIGHT, FRONT, BACK;

    Dice4(int[] a) {
        this.TOP = a[0];
        this.FRONT = a[1];
        this.RIGHT = a[2];
        this.LEFT = a[3];
        this.BACK = a[4];
        this.BOTTOM = a[5];
    }

    public boolean superEquals(Dice4 another) {
        Dice4 tmp = another;

        while (true) {
            if (this.equalsMethod(tmp)) {
                break;
            }
            tmp.turnN();
            if (this.equalsMethod(tmp)) {
                break;
            }
            tmp.turnN();
            if (this.equalsMethod(tmp)) {
                break;
            }
            tmp.turnN();
            if (this.equalsMethod(tmp)) {
                break;
            }
            tmp.turnW();
            if (this.equalsMethod(tmp)) {
                break;
            }
            tmp.turnE();
            tmp.turnE();
            if (this.equalsMethod(tmp)) {
                break;
            }
            return false;
        }
        return true;
    }

    boolean equalsMethod(Dice4 another) {
        Dice4 tmp = another;
        if (this.TOP == tmp.TOP) {
            if (this.BOTTOM == tmp.BOTTOM) {
                for (int i = 0; i < 4; i++) {
                    if (this.checkSides(tmp)) {
                        return true;
                    }
                    tmp.turnR();
                }
            }
        }
        return false;
    }

    boolean checkSides(Dice4 another) {
        // TODO 自動生成されたメソッド・スタブ
        return this.FRONT == another.FRONT && this.RIGHT == another.RIGHT && this.LEFT == another.LEFT
                && this.BACK == another.BACK;
    }

    void turnS() {
        int tmp = this.TOP;
        this.TOP = this.BACK;
        this.BACK = this.BOTTOM;
        this.BOTTOM = this.FRONT;
        this.FRONT = tmp;
    }

    void turnN() {
        int tmp = this.TOP;
        this.TOP = this.FRONT;
        this.FRONT = this.BOTTOM;
        this.BOTTOM = this.BACK;
        this.BACK = tmp;
    }

    void turnW() {
        int tmp = this.TOP;
        this.TOP = this.RIGHT;
        this.RIGHT = this.BOTTOM;
        this.BOTTOM = this.LEFT;
        this.LEFT = tmp;
    }

    void turnE() {
        int tmp = this.TOP;
        this.TOP = this.LEFT;
        this.LEFT = this.BOTTOM;
        this.BOTTOM = this.RIGHT;
        this.RIGHT = tmp;
    }

    void turnL() {
        int tmp = this.FRONT;
        this.FRONT = this.RIGHT;
        this.RIGHT = this.BACK;
        this.BACK = this.LEFT;
        this.LEFT = tmp;
    }

    void turnR() {
        int tmp = this.FRONT;
        this.FRONT = this.LEFT;
        this.LEFT = this.BACK;
        this.BACK = this.RIGHT;
        this.RIGHT = tmp;
    }
}