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
  def initialize num_dict
    @num=num_dict

    @top=1
    @bottom=6
    @right=3
    @left=4
    @forward=5
    @backward=2

  end

  def ==(other)
    checkSameDice(other)
  end

  def checkSameDice(other)
    1.upto 6 do |i|
      setTop i 
      4.times do
        counterClockWiseRot
        return true if checkSameNumDice(other) 
      end
    end
    false
  end

  def checkSameNumDice(other)
    otherNum=other.instance_variable_get(:@num)
    if ( (@num[@top]==otherNum[other.instance_variable_get('@top')])&&(@num[@bottom]==otherNum[other.instance_variable_get('@bottom')])&&(@num[@right]==otherNum[other.instance_variable_get('@right')])&&(@num[@left]==otherNum[other.instance_variable_get('@left')])&&(@num[@forward]==otherNum[other.instance_variable_get('@forward')])&&(@num[@backward]==otherNum[other.instance_variable_get('@backward')]) )
      return true
    else
      return false
    end
  end

  def counterClockWiseRot
    temp=@right
    @right=@backward
    @backward=@left
    @left=@forward
    @forward=temp
  end

  def to_s
    <<"EOS"
    top:      #{@num[@top]}
    bottom:   #{@num[@bottom]}
    right:    #{@num[@right]}
    left:     #{@num[@left]}
    forward:  #{@num[@forward]}
    backward: #{@num[@backward]}

EOS
  end

  def getTop
    @num[@top]
  end

  def moveE
    temp=@top
    @top=@left
    @left=@bottom
    @bottom=@right
    @right=temp
  end

  def setTop(top)
    4.times {
      return true if @top==top
      moveN
    }
    counterClockWiseRot
    4.times {
      return true if @top==top
      moveN
    }
    false
    end

  def setRight(rightNum)
    top=@num.key(rightNum)
    3.times do |i|
      break if @top==top
      moveE
      moveN if @top!=top
    end
    if @top==top
      moveE
      return true
    end
    false
  end
    
  def moveW
    temp=@top
    @top=@right
    @right=@bottom
    @bottom=@left
    @left=temp
  end

  def moveN
    temp=@top
    @top=@backward
    @backward=@bottom
    @bottom=@forward
    @forward=temp
  end
  
  def moveS
    temp=@top
    @top=@forward
    @forward=@bottom
    @bottom=@backward
    @backward=temp
  end

  def rotate(char)
    case char
      when "E"
        moveE
      when "W"
        moveW
      when "N"
        moveN
      when "S"
        moveS
    end
  end

  def setBackwardandRight(backNum,rightNum)
    back=@num.key(backNum)
    right=@num.key(rightNum)
    3.times{
      break if @backward==back
      moveN
    }
    if @backward!=back
      moveE
      while @backward!=back
        moveN
      end
    end
 
    while @right!=right
      moveE
    end
  end
end

def newDiceFromInput
  a,b,c,d,e,f=STDIN.gets.split(" ")
  Dice.new({1 => a.to_i , 2 => b.to_i , 3 => c.to_i , 4 => d.to_i , 5 => e.to_i , 6 => f.to_i})
end

num=STDIN.gets.to_i
dices=[]
num.times do
  dices<<newDiceFromInput
end
noFlag=false
dices.each_with_index do |dice,i|
  dices.each_with_index  do |other,j|
    next if i==j
    noFlag=true if dice==other
  end
end
if noFlag
  puts "No"
else
  puts "Yes"
end