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 Python3 (judge verdict: Wrong Answer)

class Dice(object):
 
    def __init__(self, d):

        self.rows = [d[0], d[4], d[5], d[1]]
        self.cols = [d[0], d[2], d[5], d[3]]
 
    def move_next_rows(self):
        temp = self.rows.pop(0)
        self.rows.append(temp)
        self.__update(self.cols, self.rows)

    def move_prev_rows(self):
        temp = self.rows.pop(3)
        self.rows.insert(0, temp)
        self.__update(self.cols, self.rows)
    
    def move_next_cols(self):
        temp = self.cols.pop(0)
        self.cols.append(temp)
        self.__update(self.rows, self.cols)
 
    def move_prev_cols(self):
        temp = self.cols.pop(3)
        self.cols.insert(0, temp)
        self.__update(self.rows, self.cols)

    def __update(self, x, y):
        x[0] = y[0]
        x[2] = y[2]
 
class DiceChecker(object):

    def __init__(self, dice1, dice2):
        self.dice1 = dice1
        self.dice2 = dice2
        self.dice1_top = self.dice1.rows[0]
        self.dice1_front = self.dice1.rows[3]
        
    def check_same_dice(self):
        for _ in range(4):
            for _ in range(4):
                for _ in range(4):
                    is_same_element = self.dice1.rows == self.dice2.rows and self.dice1.cols == self.dice2.cols
                    if is_same_element: 
                        return False
                    self.__rot(self.dice2)
                self.dice2.move_next_rows()
            self.dice2.move_next_cols()
            
        return True
    
    def __rot(self, dice):
        temp = dice.rows[1]
        dice.rows[1] = dice.cols[3]
        dice.cols[3] = dice.rows[3]
        dice.rows[3] = dice.cols[1]
        dice.cols[1] = temp


j = int(input())
dice_list = []
src = []
for _ in range(j):
    d = list(map(int, input().split(" ")))
    dice_list.append(Dice(d))
    src.append(Dice(d))

is_diff = False
for dice1 in dice_list:
    src.pop(0)
    for dice in src:
        dice_checker = DiceChecker(dice1, dice)
        if(dice_checker.check_same_dice()):
            is_diff = True
        else:
            is_diff = False

if is_diff:
    print("Yes")
else:
    print("No")