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 C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace _001_FindingMissingCards
{
    class Dice
    {
        private int[] num = new int[7];

        public Dice(int[] given)
        {
            num[1] = given[0];
            num[2] = given[1];
            num[3] = given[2];
            num[4] = given[3];
            num[5] = given[4];
            num[6] = given[5];
        }

        public int topNumber()
        {
            return num[1];
        }

        public int frontNumber()
        {
            return num[2];
        }
        public int rightNumber()
        {
            return num[3];
        }
        public int leftNumber()
        {
            return num[4];
        }
        public int backNumber()
        {
            return num[5];
        }

        public int bottomNumber()
        {
            return num[6];
        }

        private void moveNorth()
        {
            int tmp = num[1];
            num[1] = num[2];
            num[2] = num[6];
            num[6] = num[5];
            num[5] = tmp;
        }
        private void moveSouth()
        {
            moveNorth();
            moveNorth();
            moveNorth();
        }
        private void moveEast()
        {
            int tmp = num[1];
            num[1] = num[4];
            num[4] = num[6];
            num[6] = num[3];
            num[3] = tmp;
        }
        private void moveWest()
        {
            moveEast();
            moveEast();
            moveEast();
        }

        public void moveByCommand(char[] commands)
        {
            for (int i = 0; i < commands.Length; i++)
            {
                if (commands[i] == 'N')
                {
                    moveNorth();
                }
                else if (commands[i] == 'E')
                {
                    moveEast();
                }
                else if (commands[i] == 'W')
                {
                    moveWest();
                }
                else if (commands[i] == 'S')
                {
                    moveSouth();
                }

            }
        }

        public int getrightNumber(int topnum, int fronnum)
        {
            int x = 0;

            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }

            for (int i = 0; i < 4; i++)
            {
                for (int j = 0; j < 4; j++)
                {
                    this.moveByCommand("E".ToCharArray());

                    if (topnum == this.topNumber() && fronnum == this.frontNumber())
                    {
                        x = this.rightNumber();
                    }
                }
                this.moveByCommand("N".ToCharArray());
                if (topnum == this.topNumber() && fronnum == this.frontNumber())
                {
                    x = this.rightNumber();
                }

            }

            this.moveByCommand("EN".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("SWES".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("E".ToCharArray());
            if (topnum == this.topNumber() && fronnum == this.frontNumber())
            {
                x = this.rightNumber();
            }
            this.moveByCommand("NW".ToCharArray());
            

            return x;
        }


        public Boolean compareTo(Dice x)
        {
            Boolean ans = true;

            for (int i = 1; i < 7; i++)
            {
                for (int j = 1; j < 7; j++)
                {
                    if (this.getrightNumber(this.num[i], this.num[j]) !=
                        x.getrightNumber(this.num[i], this.num[j]))
                    {
                        ans = false;
                    }
                }
            }

            return ans;
        }
    }

    class Program
    {
        static void Main()
        {

            var numDice = Convert.ToInt32(Console.ReadLine());
            var dices = new Dice[numDice];
            for (int i = 0; i < numDice; i++)
            {
                var tmp1 = Console.ReadLine().Split(' ');
                var sample1 = new int[tmp1.Length];
                for (int j = 0; j < tmp1.Length; j++)
                {
                    sample1[j] = Convert.ToInt32(tmp1[j]);
                }
                dices[i] = new Dice(sample1);
            }

            Boolean ans = true;

            for (int i = 0; i < numDice; i++)
            {
                for (int j = i + 1; j < numDice; j++)
                {
                    if (dices[i].compareTo(dices[j]) == true)
                    {
                        ans = false;
                    }
                }
            }
            Console.WriteLine(ans ? "Yes" : "No");
        }
    }
}