Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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;

class Main{
  public static void main(String args[]) throws IOException{
   BufferedReader br = new BufferedReader(new InputStreamReader(System.in));




   int n = Integer.parseInt( br.readLine() );
   Dise[] dise = new Dise[n];

   for(int i = 0; i < n ; i++){

       String[] surface1 =  br.readLine().split(" ");
       dise[i] = new Dise();
       dise[i].setSurface(surface1);
       dise[i].SetDice(1, 2 , 3);
   }

   int matchflag = 0;
   for(int j = 0; j < n - 1; j++){
     for(int k = j + 1; k < n ; k++ ){
         if( JudgeDise(dise[j] , dise[k]) == 1 ){

             matchflag = 1;

         }

     }



   }






   if(  matchflag == 0){
       System.out.println("Yes");


   }else{
       System.out.println("No");
   }



  }


  private static int JudgeDise(Dise dise1 , Dise dise2 ){
      int x = 0;


      int matchpoint = 0;
       for(int i = 0; i < 6  ; i++){
         if(matchpoint == 3 )break;
         matchpoint = 0;
         for(int j = 0; j < 6; j++){
             if(matchpoint == 3 )break;
             matchpoint = 0;

           if(dise1.surface[i] == dise2.surface[j] ){
               dise1.RegulateDiceRight( dise1.surface[i] );//?????´???????????¢????????¢???????????????
               dise2.RegulateDiceRight( dise2.surface[j] );//?????´???????????¢????????¢???????????????

               if(dise1.surface[ dise1.Left ] == dise2.surface[ dise2.Left ] ){//?????¢??????????????????????????¢????????´????????????????????????????????????(?????£????????????????????°????????¢????????°?????????????????????????????§break?????????)
                   matchpoint++;

               }

               for(int k = 0; k < 3; k++){
                   if(dise1.surface[ dise1.Top ] == dise2.surface[ dise2.Top ] ){

                       matchpoint++;

                       break;

                   }else{

                       dise2.RollDice("N");

                   }
               }

               if(dise1.surface[ dise1.Bottom ] == dise2.surface[ dise2.Bottom ]  &&
                       dise1.surface[ dise1.Front ] == dise2.surface[ dise2.Front ] &&
                               dise1.surface[ dise1.Back ] == dise2.surface[ dise2.Back ]
                       ){

                   matchpoint ++;

               }


           }
          }

       }


       if(matchpoint==3){
          x = 1;


       }else{
           x = 0;
       }





   return x;
  }

}

class Dise{

    int[] surface = new int [6];
    int Top,Bottom,Right,Left,Front,Back;


    void setSurface(String[] SurfaceString){

        for(int i = 0; i < 6; i++){

            surface[i] = Integer.parseInt( SurfaceString[i] );

        }

    }

    void SetDice(int top, int front, int right){
       Top  = top - 1;
       Front = front - 1;
       Right = right - 1;
       Bottom = 5- (top - 1);
       Back = 5- (front - 1);
       Left = 5- (right - 1);
    }//SetDice


    void RegulateDice( int setTop, int setFront  ){


        if( surface[Left] == setTop )   {


            RollDice("E");

        }else if( surface[Right] == setTop ){

            RollDice("W");

        }else if( surface[Front] == setTop ){

            RollDice("N");

        }else if( surface[Back] == setTop ){

            RollDice("S");

        }else if( surface[Bottom] == setTop ) {

            RollDice("NN");

        }

        if( surface[Left] == setFront )   {

          RollDice("NES");

        }else if( surface[Right] == setFront ){

            RollDice("NWS");

        }else if(surface[Back]== setFront){

            RollDice("NEES");

        }


    }

    void RegulateDiceRight( int setLeft){

        if( surface[Top] == setLeft )   {

            RollDice("E");

        }else if( surface[Right] ==setLeft ){

            RollDice("EE");

        }else if( surface[Front] == setLeft ){

            RollDice("NE");

        }else if( surface[Back] == setLeft ){

            RollDice("SE");

        }else if( surface[Bottom] == setLeft ) {

            RollDice("W");

        }

    }


    void RollDice(String RollString){

        String[] SurfaceString =  RollString.split("");
        for(int i = 0; i < SurfaceString.length ; i++){

            if( SurfaceString[i].equals("W") ){

                Bottom = Left;
                Left = Top;
                Top = 5 - Bottom;
                Right = 5 - Left;

            }else if( SurfaceString[i].equals("S")){

                Bottom = Front;
                Front = Top;
                Top = 5 - Bottom;
                Back = 5 - Front;

            }else if( SurfaceString[i].equals("E")){

                Bottom = Right;
                Right = Top;
                Top = 5 - Bottom;
                Left = 5 - Right;

            }else{

                Bottom = Back;
                Back = Top;
                Top = 5 - Bottom;
                Front = 5 - Back;

            }
        }


    }//RollDice


    void lookoutDise(){

        System.out.println("TOP = :"+surface[Top] +" Bottom = :" +surface[Bottom] +" Left =:" + surface[Left] + " Right -:"+ surface[Right] + " Front =:" + surface[Front] + " Back =:" +surface[Back]) ;

    }



}