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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AOJ
{
    class Program
    {
        class Dice
        {
            int[] xIndices = new int[4];
            int[] yIndices = new int[4];
            string[] numIndicesMap = new string[6];

            public Dice()
            {
                yIndices[0] = 0;
                yIndices[1] = 1;
                yIndices[2] = 5;
                yIndices[3] = 4;

                xIndices[0] = 0;
                xIndices[1] = 3;
                xIndices[2] = 5;
                xIndices[3] = 2;

                for (int i = 0; i < numIndicesMap.Length; ++i)
                {
                    numIndicesMap[i] = (i + 1).ToString();
                }
            }
            public void SetNumberIndecesMap(string[] map)
            {
                if (map.Length != 6)
                {
                    throw new Exception("invalid mapper");
                }
                numIndicesMap = map;
            }

            static void Swap(ref int lhs, ref int rhs)
            {
                var tmp = lhs;
                lhs = rhs;
                rhs = tmp;
            }
            static void Move(int direction, ref int[] indices)
            {
                if (direction > 0)
                {
                    for (int i = 1; i < indices.Length; ++i)
                    {
                        Swap(ref indices[i - 1], ref indices[i]);
                    }
                }
                if (direction < 0)
                {
                    for (int i = indices.Length - 1; i > 0; --i)
                    {
                        Swap(ref indices[i - 1], ref indices[i]);
                    }
                }
            }
            void MoveX(int direction)
            {
                Move(direction, ref xIndices);
                yIndices[0] = xIndices[0];
                yIndices[2] = xIndices[2];
            }
            void MoveY(int direction)
            {
                Move(direction, ref yIndices);
                xIndices[0] = yIndices[0];
                xIndices[2] = yIndices[2];
            }
            public void Move(char directionCharactor)
            {
                switch (directionCharactor)
                {
                    case 'N':
                        MoveY(1);
                        return;
                    case 'S':
                        MoveY(-1);
                        return;
                    case 'E':
                        MoveX(1);
                        return;
                    case 'W':
                        MoveX(-1);
                        return;
                    default:
                        throw new Exception("invalid input");
                }
            }
            public void MoveReverse(char directionCharactor)
            {
                switch (directionCharactor)
                {
                    case 'N':
                        MoveY(-1);
                        return;
                    case 'S':
                        MoveY(1);
                        return;
                    case 'E':
                        MoveX(-1);
                        return;
                    case 'W':
                        MoveX(1);
                        return;
                    default:
                        throw new Exception("invalid input");
                }
            }

            public string Top
            {
                get
                {
                    return numIndicesMap[xIndices[0]];
                }
            }
            public string Bottom
            {
                get
                {
                    return numIndicesMap[xIndices[2]];
                }
            }
            public string Right
            {
                get
                {
                    return numIndicesMap[xIndices[3]];
                }
            }
            public string Left
            {
                get
                {
                    return numIndicesMap[xIndices[1]];
                }
            }
            public string Front
            {
                get
                {
                    return numIndicesMap[yIndices[1]];
                }
            }
            public string Back
            {
                get
                {
                    return numIndicesMap[yIndices[3]];
                }
            }
        }

        class DiceComparetor
        {
            class Snap
            {
                public string[] faces = new string[6];

                public Snap(Dice dice)
                {
                    faces[0] = dice.Top;
                    faces[1] = dice.Bottom;
                    faces[2] = dice.Right;
                    faces[3] = dice.Left;
                    faces[4] = dice.Front;
                    faces[5] = dice.Back;
                }

                public override bool Equals(object obj)
                {
                    var rhs = obj as Snap;
                    if (rhs == null) return false;
                    for (int i = 0; i < faces.Length; ++i)
                    {
                        if (faces[i].Equals(rhs.faces[i]) == false)
                        {
                            return false;
                        }
                    }
                    return true;
                }
                public override int GetHashCode()
                {
                    int hash = 0;
                    foreach (var f in faces)
                    {
                        hash = f.GetHashCode();
                    }
                    return hash;
                }
            }

            char[] moves = new char[4] { 'N', 'S', 'E', 'W' };
            HashSet<Snap> traversedChecker = new HashSet<Snap>();
            int maxDepth = 0;   // デバッグ用
            int checkCount = 0; // デバッグ用

            public Dice dice;

            public void traverse(int depth)
            {
                maxDepth = Math.Max(maxDepth, depth);

                for (int i = 0; i < moves.Length; ++i)
                {
                    dice.Move(moves[i]);
                    var snap = new Snap(dice);
                    if (traversedChecker.Contains(snap))
                    {
                        continue;
                    }
                    traversedChecker.Add(snap);

                    ++checkCount;
                    traverse(depth + 1);

                    dice.MoveReverse(moves[i]);
                }
            }

            public bool isSame(Dice dice)
            {
                var snap = new Snap(dice);
                return traversedChecker.Contains(snap);
            }
        }
        static bool isSameDice(string[] indicesMapper0, string[] indicesMapper1)
        {
            var dice0 = new Dice();
            dice0.SetNumberIndecesMap(indicesMapper0);

            var dice1 = new Dice();
            dice1.SetNumberIndecesMap(indicesMapper1);

            var comparator = new DiceComparetor { dice = dice0 };
            comparator.traverse(0);
            return comparator.isSame(dice1);
        }
        static bool isAllDifferentDice(List<string[]> indicesMappers)
        {
            var dice0 = new Dice();
            dice0.SetNumberIndecesMap(indicesMappers.First());

            var comparator = new DiceComparetor { dice = dice0 };
            comparator.traverse(0);

            for (int i = 1; i < indicesMappers.Count; ++i)
            {
                var dice = new Dice();
                dice.SetNumberIndecesMap(indicesMappers[i]);
                if (comparator.isSame(dice))
                {
                    return false;
                }
            }

            return true;
        }

        static void Main(string[] args)
        {
            var count = int.Parse(Console.In.ReadLine());
            var indicesMappers = new List<string[]>();
            for (int i = 0; i < count; ++i)
            {
                indicesMappers.Add(Console.In.ReadLine().Split(' ').ToArray());
            }

            var result = "No";
            if (isAllDifferentDice(indicesMappers))
            {
                result = "Yes";
            }

            Console.Out.WriteLine(result);
        }
    }
}