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: Accepted)

class Dice      
    @face = nil         
                        
    def initialize ary   
        @face = ary        
    end                     

    def top
        @face[0]
    end

    def rotate news     
        f = @face.dup
        case news
        when "N"
            @face = [f[1],f[5],f[2],f[3],f[0],f[4]]
        when "E"
            @face = [f[3],f[1],f[0],f[5],f[4],f[2]]
        when "W"
            @face = [f[2],f[1],f[5],f[0],f[4],f[3]]
        when "S"
            @face = [f[4],f[0],f[2],f[3],f[5],f[1]]
        end
    end

    def right top,front
        "SWSWS".each_char do |c|
            if @face[0] == top
                break 
            end
            rotate c
        end
        rotate "N"
        "WWW".each_char do |c|
            if @face[0] == front
                break 
            end
            rotate c
        end
    @face[2]
    end

    def same? face2
        return true if @face == face2
        "WWWWSWWWWSWWWWSWWWWSWWWWSWWW".each_char { |c|
            rotate c
            return true if @face == face2
        }
        return false
    end
end

lines = []
n = gets.to_i
n.times {lines << gets.chomp.split}

differ = true
for i in 0..n-2
    for j in i + 1..n-1
        if Dice.new(lines[i]).same?(lines[j])
            differ = false
            break
        end
    end
end
puts differ ? "Yes" : "No"