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: Time Limit Exceeded)

class Dice
  attr_accessor :faces

  # |T F L|
  # |B U R|
  def initialize(faces)
    top, front, right, left, back, bottom = faces
    @faces = [[top, bottom], [front, back], [left, right]]
  end

  def move(commands)
    commands.split('').each do |com|
      case com.upcase.to_sym
      when :E
        faces[0], faces[2] = faces[2], faces[0].reverse
      when :W
        faces[0], faces[2] = faces[2].reverse, faces[0]
      when :N
        faces[0], faces[1] = faces[1], faces[0].reverse
      when :S
        faces[0], faces[1] = faces[1].reverse, faces[0]
      end
    end
  end

  def method_missing(face)
    if %i(top bottom front back left right).include? face
      {
        top:    faces[0][0],
        bottom: faces[0][1],
        front:  faces[1][0],
        back:   faces[1][1],
        left:   faces[2][0],
        right:  faces[2][1]
      }[face]
    else
      super
    end
  end

  def ==(other)
    commands = (["N"]*3 + ["E"]*3)
    0.upto(commands.size) do |r|
      commands.permutation(r).each do |c|
        move(c.join)
        return true if faces == other.faces
      end
    end
    false
  end

  def clone
    self.class.new([top, front, right, left, back, bottom])
  end

  def info
    p({ T: top, F: front, R: right, L: left, U: back, B: bottom })
  end
end

$stdin = DATA if $<.eof?

gets

dices = ARGF.each.map do |line|
  Dice.new(line.split)
end

match = dices.combination(2).any? do |da, db|
  da == db
end

puts(match ? "No" : "Yes")