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 Ruby (judge verdict: Wrong Answer)

class Dice
    def dice_s(arr, i)
        arr[i][0],arr[i][1],arr[i][4],arr[i][5] = arr[i][4],arr[i][0],arr[i][5],arr[i][1]
        return arr[i]
    end
 
    def dice_e(arr, i)
        arr[i][0],arr[i][2],arr[i][3],arr[i][5] = arr[i][3],arr[i][0],arr[i][5],arr[i][2]
        return arr[i]
    end
 
    def dice_w(arr, i)
        arr[i][0],arr[i][2],arr[i][3],arr[i][5] = arr[i][2],arr[i][5],arr[i][0],arr[i][3]
        return arr[i]
    end
 
    def dice_n(arr, i)
        arr[i][0],arr[i][1],arr[i][4],arr[i][5] = arr[i][1],arr[i][5],arr[i][0],arr[i][4]
        return arr[i]
    end
 
    def dice_b(arr, i)
        arr[i][0],arr[i][1],arr[i][4],arr[i][5]  = arr[i][5],arr[i][4],arr[i][1],arr[i][0]
        return arr[i]
    end
 
    def dice_sp(arr, i)
        arr[i][1],arr[i][2],arr[i][4],arr[i][3] = arr[i][2],arr[i][4],arr[i][3],arr[i][1]
        return arr[i]
    end
end

n = gets.chomp.to_i
arr = Array.new(6){Array.new(n)}
arr[0] = gets.chomp.split.map(&:to_i)
count = false
dice = Dice.new()

for i in 1..n-1
    arr[i] = gets.chomp.split.map(&:to_i)
    
    case arr[0][0]
    when arr[i][4]; dice.dice_s(arr, i)
    when arr[i][3]; dice.dice_e(arr, i)
    when arr[i][2]; dice.dice_w(arr, i)
    when arr[i][1]; dice.dice_n(arr, i)
    when arr[i][5]; dice.dice_b(arr, i)
    end

    while arr[0][1] != arr[i][1]
        dice.dice_sp(arr, i)
    end

    break if arr[0] == arr[i]

    next if i < n-1

    catch(:break) do
        for j in 1..n-1
            for k in j+1..n-1
                throw :break if arr[j] == arr[k]
            end
        end
    end
end

puts count ? "No" : "Yes"