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 PHP (judge verdict: Accepted)

<?php

namespace egg1to3;

class Dice
{
    protected $top;
    protected $front;
    protected $left;
    protected $right;
    protected $back;
    protected $bottom;
    protected $save;

    public function __construct($arr)
    {
        $this->save = $arr;
        $this->init();
    }

    public function init()
    {
        foreach ($this->save as $key => $val) {
            $this->{$key} = (int)$val;
        }
    }

    public function parse($str)
    {
        for ($i = 0, $len = strlen($str); $i < $len; $i++) {
            $direction = $str[$i];
            $this->move($direction);
        }
    }

    //指定された面を上面に移動させる
    public function positionChange($from)
    {
        switch ($from) {
            case 'top':
                break;
            case 'front':
                $this->move('N');
                break;
            case 'right':
                $this->move('W');
                break;
            case 'left':
                $this->move('E');
                break;
            case 'back':
                $this->move('S');
                break;
            case 'bottom':
                $this->parse('NN');
                break;
        }
    }

    //90度回転させる
    public function rotate($left = false)
    {
        $this->parse($left ? 'NES' : 'NWS');
    }

    //指定された面の値を取得
    public function getNumber($from)
    {
        return $this->{$from};
    }

    //面の値を配列にして返す
    public function getArray()
    {
        $arr = array();
        foreach ($this as $key => $val) {
            if (preg_match('/top|front|right|left|back|bottom/', $key)) {
                $arr[$key] = $val;
            }
        }
        return $arr;
    }

    //同じサイコロかチェック
    public function isEqual($dice)
    {
        $arr1 = $this->getArray();
        $arr2 = $dice->getArray();
        $diff = array_diff($arr1, $arr2);
        //片方にしか存在しない値がある
        if (count($diff)) {
            return false;
        }

        $keys = explode(',', 'top,front,right,left,back,bottom');
        foreach ($keys as $key) {
            //ある面を上面に移動する
            $dice->positionChange($key);
            $cnt = 0;
            //前面を同じ値にする(合わなければ一致しない)
            while ($this->front !== $dice->getNumber('front')) {
                //前面を同じ値にできなかった
                if ($cnt++ === 4) {
                    break;
                }
                $dice->rotate();
            }

            //初期化して次の面へ
            if ($cnt === 4) {
                $dice->init();
                continue;
            }

            $arr2 = $dice->getArray();
            $diff = array_diff_assoc($arr1, $arr2);
            //全ての面が一致すれば返り値は0
            if (count($diff) === 0) {
                return true;
            }

            $dice->init();
        }

        //一致しなかった
        return false;
    }

    protected function move($direction)
    {
        $top = $this->top;
        switch ($direction) {
            case 'S':
                $this->top = $this->back;
                $this->back = $this->bottom;
                $this->bottom = $this->front;
                $this->front = $top;
                break;
            case 'N':
                $this->top = $this->front;
                $this->front = $this->bottom;
                $this->bottom = $this->back;
                $this->back = $top;
                break;
            case 'E':
                $this->top = $this->left;
                $this->left = $this->bottom;
                $this->bottom = $this->right;
                $this->right = $top;
                break;
            case 'W':
                $this->top = $this->right;
                $this->right = $this->bottom;
                $this->bottom = $this->left;
                $this->left = $top;
                break;
            default:
                new Error('error');
        }
    }
}

fscanf(STDIN, '%d', $n);
$line = trim(fgets(STDIN));
$nums = explode(' ', $line);
$keys = explode(',', 'top,front,right,left,back,bottom');
$arr = array_combine($keys, $nums);
$base = new Dice($arr);
$bool = false;

for ($i = 1; $i < $n; $i++) {
    $line = trim(fgets(STDIN));
    //既に同じサイコロがある
    if ($bool) {
        continue;
    }

    $nums = explode(' ', $line);
    $arr = array_combine($keys, $nums);
    $dice = new Dice($arr);
    if ($base->isEqual($dice)) {
        $bool = true;
    }
}

echo $bool ? "No\n" : "Yes\n";