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
  attr_reader :labels

  def initialize(args)
    @labels = args
  end

  def top
    @labels[0]
  end

  def move(a,b,c,d)
    arr = [@labels[a], @labels[b], @labels[c], @labels[d]]
    t = arr.shift
    arr << t
    @labels[a], @labels[b], @labels[c], @labels[d] = arr
  end

  def move_n
    move(0,1,5,4)
  end

  def move_e
    move(0,3,5,2)
  end

  def move_s
    move(4,5,1,0)
  end

  def move_w
    move(2,5,3,0)
  end

  def move_to_input(ch)
    case ch
    when 'E'
      move_e
    when 'N'
      move_n
    when 'S'
      move_s
    when 'W'
      move_w
    end
  end
end

n = gets.to_i
dices = []
n.times do
  input = gets.split.map(&:to_i)
  dices << Dice.new(input)
end

f = 'Yes'

dices.combination(2) do |dice1, dice2|
  100.times do
    dice2.move_to_input('ENSW'.chars.sample)
    if dice1.labels == dice2.labels
      f = 'No'
      break
    end
  end
end

puts f