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.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
 
 
public class Main {
    public static void main(String[] args) throws Exception {
 
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int diceCount = Integer.parseInt(br.readLine());
 
        List<Dice> diceList = new ArrayList<Dice>();
        for (int i = 0; i < diceCount; i++) {
 
            String[] line = br.readLine().split(" ");
            int[] data = new int[line.length];
            for (int d = 0; d < data.length; d++) {
                data[d] = Integer.parseInt(line[d]);
            }
            Dice dice = new Dice(data);
            diceList.add(dice);
        }
 
        boolean result;
        for (int d1 = 0; d1 < diceList.size() - 1; d1++) {
            for (int d2 = d1 + 1; d2 < diceList.size(); d2++) {
                 result = isSameDice(diceList.get(d1), diceList.get(d2));
 
                 if (result) {
                     System.out.println("No");
                     return;
                 }
            }
        }
        System.out.println("Yes");
    }
 
    public static boolean isSameDice(Dice d1, Dice d2) {
        String[] allPosList = {"top", "bottom", "left", "right", "front", "back"};
 
        for (int p = 0; p < allPosList.length; p++) {
            d1.moveToTop(allPosList[p]);
            String[] topPosList = d2.getPosList(d1.getData("top"));
            for (int i = 0; i < topPosList.length; i++) {
                d2.moveToTop(topPosList[i]);
 
                String[] frontPosList = d2.getPosList(d1.getData("front"));
                for (int j = 0; j < frontPosList.length; j++) {
                    d2.spinToFront(frontPosList[j]);
 
                    if (d1.getAllData().equals(d2.getAllData())) {
                        return true;
                    }
                }
            }
        }
        return false;
    }
}
 
class Dice {
    HashMap<String, Integer> pos;
    Dice(int[] data) {
        pos = new HashMap<String, Integer>();
        pos.put("top"   , data[1 - 1]);
        pos.put("bottom", data[6 - 1]);
        pos.put("left"  , data[4 - 1]);
        pos.put("right" , data[3 - 1]);
        pos.put("front" , data[2 - 1]);
        pos.put("back"  , data[5 - 1]);
    }
 
    public String[] getPosList(int data) {
        List<String> posList = new ArrayList<String>();
        Iterator<HashMap.Entry<String, Integer>> ite = pos.entrySet().iterator();
        while(ite.hasNext()) {
            Map.Entry<String, Integer> entry = ite.next();
 
            if (data == entry.getValue()) {
                posList.add(entry.getKey());
            }
        }
 
        return posList.toArray(new String[posList.size()]);
    }
 
    public void moveToTop(String currentPos) {
        switch (currentPos) {
        case "top":
            break;
 
        case "bottom":
            roll('S');
            roll('S');
            break;
 
        case "left":
            roll('E');
            break;
 
        case "right":
            roll('W');
            break;
 
        case "front":
            roll('N');
            break;
 
        case "back":
            roll('S');
            break;
        }
    }
 
    public void spinToFront(String currentPos) {
        switch (currentPos) {
        case "front":
            break;
 
        case "bottom":
            break;
 
        case "right":
            spin('R');
            break;
 
        case "left":
            spin('L');
            break;
 
        case "back":
            spin('L');
            spin('L');
            break;
        }
    }
 
    public void roll(char m) {
        int temp = -1;
        switch (m) {
        case 'N':
            temp = pos.get("top");
            pos.put("top"   , pos.get("front"));
            pos.put("front" , pos.get("bottom"));
            pos.put("bottom", pos.get("back"));
            pos.put("back"  , temp);
 
            break;
 
        case 'E':
            temp = pos.get("top");
            pos.put("top"    , pos.get("left"));
            pos.put("left"   , pos.get("bottom"));
            pos.put("bottom" , pos.get("right"));
            pos.put("right"  , temp);
 
            break;
 
        case 'W':
            temp = pos.get("top");
            pos.put("top"    , pos.get("right"));
            pos.put("right"  , pos.get("bottom"));
            pos.put("bottom" , pos.get("left"));
            pos.put("left"   , temp);
 
            break;
 
        case 'S':
            temp = pos.get("top");
            pos.put("top"    , pos.get("back"));
            pos.put("back"   , pos.get("bottom"));
            pos.put("bottom" , pos.get("front"));
            pos.put("front"  , temp);
 
            break;
        }
    }
 
    public void spin(char t) {
        int temp = -1;
        switch (t) {
        case 'L':
            temp = pos.get("front");
            pos.put("front" , pos.get("left"));
            pos.put("left"  , pos.get("back"));
            pos.put("back"  , pos.get("right"));
            pos.put("right" , temp);
 
            break;
 
        case 'R':
            temp = pos.get("front");
            pos.put("front" , pos.get("right"));
            pos.put("right" , pos.get("back"));
            pos.put("back"  , pos.get("left"));
            pos.put("left"  , temp);
 
            break;
        }
    }
 
    public int getData(String p) {
        return pos.get(p);
    }
 
    public String getAllData() {
        StringBuilder sb = new StringBuilder();
        sb.append(pos.get("top")).append(" ");
        sb.append(pos.get("bottom")).append(" ");
        sb.append(pos.get("left")).append(" ");
        sb.append(pos.get("right")).append(" ");
        sb.append(pos.get("front")).append(" ");
        sb.append(pos.get("back"));
 
        return sb.toString();
    }
}